Invariants from classical field theory
Diaz, Rafael
2007-01-01
We introduce a method that generates invariant functions from classical field theories depending on external parameters. We apply our method to several field theories such as abelian BF, Chern-Simons and 2-dimensional Yang-Mills theory.
Knot Invariants from Classical Field Theories
Leal, L C
1999-01-01
We consider the Non-Abelian Chern-Simons term coupled to external particles, in a gauge and diffeomorphism invariant form. The classical equations of motion are perturbativelly studied, and the on-shell action is shown to produce knot-invariants associated with the sources. The first contributions are explicitly calculated, and the corresponding knot-invariants are recognized. We conclude that the interplay between Knot Theory and Topological Field Theories is manifested not only at the quantum level, but in a classical context as well.
Polynomial Invariant Theory of the Classical Groups
Westrich, Quinton
2011-01-01
The goal of invariant theory is to find all the generators for the algebra of representations of a group that leave the group invariant. Such generators will be called \\emph{basic invariants}. In particular, we set out to find the set of basic invariants for the classical groups GL$(V)$, O$(n)$, and Sp$(n)$ for $n$ even. In the first half of the paper we set up relevant definitions and theorems for our search for the set of basic invariants, starting with linear algebraic groups and then discussing associative algebras. We then state and prove a monumental theorem that will allow us to proceed with hope: it says that the set of basic invariants is finite if $G$ is reductive. Finally we state without proof the First Fundamental Theorems, which aim to list explicitly the relevant sets of basic invariants, for the classical groups above. We end by commenting on some applications of invariant theory, on the history of its development, and stating a useful theorem in the appendix whose proof lies beyond the scope ...
Evolving Planck Mass in Classically Scale-Invariant Theories
Kannike, K; Spethmann, C; Veermäe, H
2016-01-01
We consider classically scale-invariant theories with non-minimally coupled scalar fields, where the Planck mass and the hierarchy of physical scales are dynamically generated. The classical theories possess a fixed point, where scale invariance is spontaneously broken. In these theories, however, the Planck mass becomes unstable in the presence of explicit sources of scale invariance breaking, such as non-relativistic matter and cosmological constant terms. We quantify the constraints on such classical models from Big Bang Nucleosynthesis that lead to an upper bound on the non-minimal coupling and require trans-Planckian field values. We show that quantum corrections to the scalar potential can stabilise the fixed point close to the minimum of the Coleman-Weinberg po- tential. The time-averaged motion of the evolving fixed point is strongly suppressed, thus the limits on the evolving gravitational constant from Big Bang Nucleosynthesis and other measurements do not presently constrain this class of theories....
Link Invariants from Classical Chern-Simons Theory
Leal, L C
2002-01-01
Taking as starting point a perturbative study of the classical equations of motion of the non-Abelian Chern-Simons Theory with non-dynamical sources, we search for analytical expressions for link invarians. In order to present this expressions in a manifestly diffeomorphism-invariant form, we introduce a set of differential forms associated with submanifolds in Euclidean three-space that allow us to write the link invariants as a kind of surface-dependent diffeomorphism-invariants that present certain Abelian gauge symmetry.
Classical morphology of plants as an elementary instance of classical invariant theory.
Directory of Open Access Journals (Sweden)
Evgeny V Mavrodiev
Full Text Available It has long been known that structural chemistry shows an intriguing correspondence with Classical Invariant Theory (CIT. Under this view, an algebraic binary form of the degree n corresponds to a chemical atom with valence n and each physical molecule or ion has an invariant-theoretic counterpart. This theory was developed using the Aronhold symbolical approach and the symbolical processes of convolution/transvection in CIT was characterized as a potential "accurate morphological method". However, CIT has not been applied to the formal morphology of living organisms. Based on the morphological interpretation of binary form, as well as the process of convolution/transvection, the First and Second Fundamental Theorems of CIT and the Nullforms of CIT, we show how CIT can be applied to the structure of plants, especially when conceptualized as a series of plant metamers (phytomers. We also show that the weight of the covariant/invariant that describes a morphological structure is a criterion of simplicity and, therefore, we argue that this allows us to formulate a parsimonious method of formal morphology. We demonstrate that the "theory of axilar bud" is the simplest treatment of the grass seedling/embryo. Our interpretations also represent Troll's bauplan of the angiosperms, the principle of variable proportions, morphological misfits, the basic types of stem segmentation, and Goethe's principle of metamorphosis in terms of CIT. Binary forms of different degrees might describe any repeated module of plant organisms. As bacteria, invertebrates, and higher vertebrates are all generally shared a metameric morphology, wider implications of the proposed symmetry between CIT and formal morphology of plants are apparent.
Surface-Invariants in 2D Classical Yang-Mills Theory
Díaz, R; Leal, L; D\\'{\\i}az, Rafael; Leal, Lorenzo
2006-01-01
We study a method to obtain invariants under area-preserving diffeomorphisms associated to closed curves in the plane from classical Yang-Mills theory in two dimensions. Taking as starting point the Yang-Mills field coupled to non dynamical particles carrying chromo-electric charge, and by means of a perturbative scheme, we obtain the first two contributions to the on shell action, which are area-invariants. A geometrical interpretation of these invariants is given.
Energy Technology Data Exchange (ETDEWEB)
Lakhno, V. D., E-mail: lak@impb.psn.ru [Russian Academy of Sciences, Institute of Mathematical Problems of Biology (Russian Federation)
2013-06-15
A physical interpretation of translation-invariant polarons and bipolarons is presented, some results of their existence are discussed. Consideration is given to the problem of quantization in the vicinity of the classical solution in the quantum field theory. The lowest variational estimate is obtained for the bipolaron energy E({eta}) with E(0) = -0.440636{alpha}{sup 2}, where {alpha} is a constant of electron-phonon coupling, {eta} is a parameter of ion binding.
Powell, Stephen; Chalker, J. T.
2008-10-01
We derive a continuum theory for the phase transition in a classical dimer model on the cubic lattice, observed in recent Monte Carlo simulations. Our derivation relies on the mapping from a three-dimensional classical problem to a two-dimensional quantum problem, by which the dimer model is related to a model of hard-core bosons on the kagome lattice. The dimer-ordering transition becomes a superfluid Mott insulator quantum phase transition at fractional filling, described by an SU(2)-invariant continuum theory.
Computational invariant theory
Derksen, Harm
2015-01-01
This book is about the computational aspects of invariant theory. Of central interest is the question how the invariant ring of a given group action can be calculated. Algorithms for this purpose form the main pillars around which the book is built. There are two introductory chapters, one on Gröbner basis methods and one on the basic concepts of invariant theory, which prepare the ground for the algorithms. Then algorithms for computing invariants of finite and reductive groups are discussed. Particular emphasis lies on interrelations between structural properties of invariant rings and computational methods. Finally, the book contains a chapter on applications of invariant theory, covering fields as disparate as graph theory, coding theory, dynamical systems, and computer vision. The book is intended for postgraduate students as well as researchers in geometry, computer algebra, and, of course, invariant theory. The text is enriched with numerous explicit examples which illustrate the theory and should be ...
Palmer, T N
2016-01-01
Invariant Set Theory (IST) is a realistic, locally causal theory of fundamental physics which assumes a much stronger synergy between cosmology and quantum physics than exists in contemporary theory. In IST the (quasi-cyclic) universe $U$ is treated as a deterministic dynamical system evolving precisely on a measure-zero fractal invariant subset $I_U$ of its state space. In this approach, the geometry of $I_U$, and not a set of differential evolution equations in space-time $\\mathcal M_U$, provides the most primitive description of the laws of physics. As such, IST is non-classical. The geometry of $I_U$ is based on Cantor sets of space-time trajectories in state space, homeomorphic to the algebraic set of $p$-adic integers, for large but finite $p$. In IST, the non-commutativity of position and momentum observables arises from number theory - in particular the non-commensurateness of $\\phi$ and $\\cos \\phi$. The complex Hilbert Space and the relativistic Dirac Equation respectively are shown to describe $I_U$...
Inflation and classical scale invariance
Racioppi, Antonio
2014-01-01
BICEP2 measurement of primordial tensor modes in CMB suggests that cosmological inflation is due to a slowly rolling inflaton taking trans-Planckian values and provides further experimental evidence for the absence of large $M_{\\rm P}$ induced operators. We show that classical scale invariance solves the problem and allows for a remarkably simple scale-free inflaton model without any gauge group. Due to trans-Planckian inflaton values and VEVs, a dynamically induced Coleman-Weinberg-type inflaton potential of the model can predict tensor-to-scalar ratio $r$ in a large range. Precise determination of $r$ in future experiments will allow to test the proposed field-theoretic framework.
Supersymmetric invariant theories
Esipova, S R; Radchenko, O V
2013-01-01
We study field models for which a quantum action (i.e. the action appearing in the generating functional of Green functions) is invariant under supersymmetric transformations. We derive the Ward identity which is direct consequence of this invariance. We consider a change of variables in functional integral connected with supersymmetric transformations when its parameter is replaced by a nilpotent functional of fields. Exact form of the corresponding Jacobian is found. We find restrictions on generators of supersymmetric transformations when a consistent quantum description of given field theories exists.
Supersymmetric invariant theories
Esipova, S. R.; Lavrov, P. M.; Radchenko, O. V.
2014-04-01
We study field models for which a quantum action (i.e. the action appearing in the generating functional of Green functions) is invariant under supersymmetric transformations. We derive the Ward identity which is a direct consequence of this invariance. We consider a change of variables in functional integral connected with supersymmetric transformations when its parameter is replaced by a nilpotent functional of fields. Exact form of the corresponding Jacobian is found. We find restrictions on generators of supersymmetric transformations when a consistent quantum description of given field theories exists.
Hidden invariance of the free classical particle
García, S
1993-01-01
A formalism describing the dynamics of classical and quantum systems from a group theoretical point of view is presented. We apply it to the simple example of the classical free particle. The Galileo group $G$ is the symmetry group of the free equations of motion. Consideration of the free particle Lagrangian semi-invariance under $G$ leads to a larger symmetry group, which is a central extension of the Galileo group by the real numbers. We study the dynamics associated with this group, and characterize quantities like Noether invariants and evolution equations in terms of group geometric objects. An extension of the Galileo group by $U(1)$ leads to quantum mechanics.
Fast forward to the classical adiabatic invariant
Jarzynski, Christopher; Patra, Ayoti; Subaşı, Yiğit
2016-01-01
We show how the classical action, an adiabatic invariant, can be preserved under non-adiabatic conditions. Specifically, for a time-dependent Hamiltonian $H = p^2/2m + U(q,t)$ in one degree of freedom, and for an arbitrary choice of action $I_0$, we construct a "fast-forward" potential energy function $V_{\\rm FF}(q,t)$ that, when added to $H$, guides all trajectories with initial action $I_0$ to end with the same value of action. We use this result to construct a local dynamical invariant $J(q,p,t)$ whose value remains constant along these trajectories. We illustrate our results with numerical simulations. Finally, we sketch how our classical results may be used to design approximate quantum shortcuts to adiabaticity.
Potential Theory in Classical Electrodynamics
Engelhardt, Wolfgang
2012-01-01
In Maxwell's classical theory of electrodynamics the fields are frequently expressed by potentials in order to facilitate the solution of the first order system of equations. This method obscures, however, that there exists an inconsistency between Faraday's law of induction and Maxwell's flux law. As a consequence of this internal contradiction there is neither gauge invariance, nor exist unique solutions in general. It is also demonstrated that inhomogeneous wave equations cannot be solved by retarded integrals.
Advanced classical field theory
Giachetta, Giovanni; Sardanashvily, Gennadi
2009-01-01
Contemporary quantum field theory is mainly developed as quantization of classical fields. Therefore, classical field theory and its BRST extension is the necessary step towards quantum field theory. This book aims to provide a complete mathematical foundation of Lagrangian classical field theory and its BRST extension for the purpose of quantization. Based on the standard geometric formulation of theory of nonlinear differential operators, Lagrangian field theory is treated in a very general setting. Reducible degenerate Lagrangian theories of even and odd fields on an arbitrary smooth manifold are considered. The second Noether theorems generalized to these theories and formulated in the homology terms provide the strict mathematical formulation of BRST extended classical field theory
Form invariance for systems of generalized classical mechanics
Institute of Scientific and Technical Information of China (English)
张毅; 梅凤翔
2003-01-01
This paper presents a form invariance of canonical equations for systems of generalized classical mechanics. According to the invariance of the form of differential equations of motion under the infinitesimal transformations, this paper gives the definition and criterion of the form invariance for generalized classical mechanical systems, and establishes relations between form invariance, Noether symmetry and Lie symmetry. At the end of the paper, an example is given to illustrate the application of the results.
Polydimensional Relativity, a Classical Generalization of the Automorphism Invariance Principle
Pezzaglia, W M
1996-01-01
The automorphism invariant theory of Crawford[J. Math. Phys. 35, 2701 (1994)] has show great promise, however its application is limited by the paradigm to the domain of spin space. Our conjecture is that there is a broader principle at work which applies even to classical physics. Specifically, the laws of physics should be invariant under polydimensional transformations which reshuffle the geometry (e.g. exchanges vectors for trivectors) but preserves the algebra. To complete the symmetry, it follows that the laws of physics must be themselves polydimensional, having scalar, vector, bivector etc. parts in one multivector equation. Clifford algebra is the natural language in which to formulate this principle, as vectors/tensors were for relativity. This allows for a new treatment of the relativistic spinning particle (the Papapetrou equations) which is problematic in standard theory. In curved space the rank of the geometry will change under parallel transport, yielding a new basis for Weyl's connection and ...
Covariantizing Classical Field Theories
López, Marco Castrillón
2010-01-01
We show how to enlarge the covariance group of any classical field theory in such a way that the resulting "covariantized" theory is 'essentially equivalent' to the original. In particular, our technique will render any classical field theory generally covariant, that is, the covariantized theory will be spacetime diffeomorphism-covariant and free of absolute objects. Our results thus generalize the well-known parametrization technique of Dirac and Kucha\\v{r}. Our constructions apply equally well to internal covariance groups, in which context they produce natural derivations of both the Utiyama minimal coupling and St\\"uckelberg tricks.
Higgs Triplet Model with Classically Conformal Invariance
Okada, Hiroshi; Yagyu, Kei
2015-01-01
We discuss an extension of the minimal Higgs triplet model with a classically conformal invariance and with a gauged $U(1)_{B-L}$ symmetry. In our scenario, tiny masses of neutrinos are generated by a hybrid contribution from the type-I and type-II seesaw mechanisms. The shape of the Higgs potential at low energies is determined by solving one-loop renormalization group equations for all the scalar quartic couplings with a set of initial values of parameters at the Planck scale. We find a successful set of the parameters in which the $U(1)_{B-L}$ symmetry is radiatively broken via the Coleman-Weinberg mechanism at the ${\\cal O}$(10) TeV scale, and the electroweak symmetry breaking is also triggered by the $U(1)_{B-L}$ breaking. Under this configuration, we can predict various low energy observables such as the mass spectrum of extra Higgs bosons, and the mixing angles. Furthermore, using these predicted mass parameters, we obtain upper limits on Yukawa couplings among an isospin triplet Higgs field and lepton...
Gauge Invariant Cosmological Perturbation Theory
Durrer, R
1993-01-01
After an introduction to the problem of cosmological structure formation, we develop gauge invariant cosmological perturbation theory. We derive the first order perturbation equations of Einstein's equations and energy momentum ``conservation''. Furthermore, the perturbations of Liouville's equation for collisionless particles and Boltzmann's equation for Compton scattering are worked out. We fully discuss the propagation of photons in a perturbed Friedmann universe, calculating the Sachs--Wolfe effect and light deflection. The perturbation equations are extended to accommodate also perturbations induced by seeds. With these general results we discuss some of the main aspects of the texture model for the formation of large scale structure in the Universe (galaxies, clusters, sheets, voids). In this model, perturbations in the dark matter are induced by texture seeds. The gravitational effects of a spherically symmetric collapsing texture on dark matter, baryonic matter and photons are calculated in first orde...
Testing gauge-invariant perturbation theory
Törek, Pascal
2016-01-01
Gauge-invariant perturbation theory for theories with a Brout-Englert-Higgs effect, as developed by Fr\\"ohlich, Morchio and Strocchi, starts out from physical, exactly gauge-invariant quantities as initial and final states. These are composite operators, and can thus be considered as bound states. In case of the standard model, this reduces almost entirely to conventional perturbation theory. This explains the success of conventional perturbation theory for the standard model. However, this is due to the special structure of the standard model, and it is not guaranteed to be the case for other theories. Here, we review gauge-invariant perturbation theory. Especially, we show how it can be applied and that it is little more complicated than conventional perturbation theory, and that it is often possible to utilize existing results of conventional perturbation theory. Finally, we present tests of the predictions of gauge-invariant perturbation theory, using lattice gauge theory, in three different settings. In ...
Dynamical String Tension in String Theory with Spacetime Weyl Invariance
Bars, Itzhak; Turok, Neil
2014-01-01
The fundamental string length, which is an essential part of string theory, explicitly breaks scale invariance. However, in field theory we demonstrated recently that the gravitational constant, which is directly related to the string length, can be promoted to a dynamical field if the standard model coupled to gravity (SM+GR) is lifted to a locally scale (Weyl) invariant theory. The higher gauge symmetry reveals previously unknown field patches whose inclusion turn the classically conformally invariant SM+GR into a geodesically complete theory with new cosmological and possibly further physical consequences. In this paper this concept is extended to string theory by showing how it can be Weyl lifted with a local scale symmetry acting on target space background fields. In this process the string tension (fundamental string length) is promoted to a dynamical field, in agreement with the parallel developments in field theory. We then propose a string theory in a geodesically complete cosmological stringy backgr...
On the Galilean Non-Invariance of Classical Electromagnetism
Preti, Giovanni; de Felice, Fernando; Masiero, Luca
2009-01-01
When asked to explain the Galilean non-invariance of classical electromagnetism on the basis of pre-relativistic considerations alone, students--and sometimes their teachers too--may face an impasse. Indeed, they often argue that a pre-relativistic physicist could most obviously have provided the explanation "at a glance", on the basis of the…
Dark matter and leptogenesis linked by classical scale invariance
Khoze, Valentin V.; Plascencia, Alexis D.
2016-11-01
In this work we study a classically scale invariant extension of the Standard Model that can explain simultaneously dark matter and the baryon asymmetry in the universe. In our set-up we introduce a dark sector, namely a non-Abelian SU(2) hidden sector coupled to the SM via the Higgs portal, and a singlet sector responsible for generating Majorana masses for three right-handed sterile neutrinos. The gauge bosons of the dark sector are mass-degenerate and stable, and this makes them suitable as dark matter candidates. Our model also accounts for the matter-anti-matter asymmetry. The lepton flavour asymmetry is produced during CP-violating oscillations of the GeV-scale right-handed neutrinos, and converted to the baryon asymmetry by the electroweak sphalerons. All the characteristic scales in the model: the electro-weak, dark matter and the leptogenesis/neutrino mass scales, are generated radiatively, have a common origin and related to each other via scalar field couplings in perturbation theory.
Dark Matter and Leptogenesis Linked by Classical Scale Invariance
Khoze, Valentin V
2016-01-01
In this work we study a classically scale invariant extension of the Standard Model that can explain simultaneously dark matter and the baryon asymmetry in the universe. In our set-up we introduce a dark sector, namely a non-Abelian SU(2) hidden sector coupled to the SM via the Higgs portal, and a singlet sector responsible for generating Majorana masses for three right-handed sterile neutrinos. The gauge bosons of the dark sector are mass-degenerate and stable, and this makes them suitable as dark matter candidates. Our model also accounts for the matter-anti-matter asymmetry. The lepton flavour asymmetry is produced during CP-violating oscillations of the GeV-scale right-handed neutrinos, and converted to the baryon asymmetry by the electroweak sphalerons. All the characteristic scales in the model: the electro-weak, dark matter and the leptogenesis/neutrino mass scales, are generated radiatively, have a common origin and related to each other via scalar field couplings in perturbation theory.
Classical scale invariance in the inert doublet model
Plascencia, Alexis D
2015-01-01
The inert doublet model (IDM) is a minimal extension of the Standard Model (SM) that can account for the dark matter in the universe. Naturalness arguments motivate us to study whether the model can be embedded into a theory with dynamically generated scales. In this work we study a classically scale invariant version of the IDM with a minimal hidden sector, which has a $U(1)_{\\text{CW}}$ gauge symmetry and a complex scalar $\\Phi$. The mass scale is generated in the hidden sector via the Coleman-Weinberg (CW) mechanism and communicated to the two Higgs doublets via portal couplings. Since the CW scalar remains light, acquires a vacuum expectation value and mixes with the SM Higgs boson, the phenomenology of this construction can be modified with respect to the traditional IDM. We analyze the impact of adding this CW scalar and the $Z'$ gauge boson on the calculation of the dark matter relic density and on the spin-independent nucleon cross section for direct detection experiments. Finally, by studying the RG ...
Isomorph invariance of the structure and dynamics of classical crystals
DEFF Research Database (Denmark)
Albrechtsen, Dan; Olsen, Andreas Elmerdahl; Pedersen, Ulf Rørbæk
2014-01-01
of a defective fcc crystal is also shown to be isomorph invariant. In contrast, a NaCl crystal model does not exhibit isomorph invariances. Other systems simulated, though in less detail, are the Wahnström binary Lennard-Jones crystal with the MgZn2 Laves crystal structure, monatomic fcc crystals of particles......This paper shows by computer simulations that some crystalline systems have curves in their thermodynamic phase diagrams, so-called isomorphs, along which structure and dynamics in reduced units are invariant to a good approximation. The crystals are studied in a classical-mechanical framework......, which is generally a good description except significantly below melting. The existence of isomorphs for crystals is validated by simulations of particles interacting via the Lennard-Jones pair potential arranged into a face-centered cubic (fcc) crystalline structure; the slow vacancy-jump dynamics...
Gauge coupling unification in a classically scale invariant model
Haba, Naoyuki; Ishida, Hiroyuki; Takahashi, Ryo; Yamaguchi, Yuya
2016-02-01
There are a lot of works within a class of classically scale invariant model, which is motivated by solving the gauge hierarchy problem. In this context, the Higgs mass vanishes at the UV scale due to the classically scale invariance, and is generated via the Coleman-Weinberg mechanism. Since the mass generation should occur not so far from the electroweak scale, we extend the standard model only around the TeV scale. We construct a model which can achieve the gauge coupling unification at the UV scale. In the same way, the model can realize the vacuum stability, smallness of active neutrino masses, baryon asymmetry of the universe, and dark matter relic abundance. The model predicts the existence vector-like fermions charged under SU(3) C with masses lower than 1 TeV, and the SM singlet Majorana dark matter with mass lower than 2.6 TeV.
Gauge coupling unification in a classically scale invariant model
Haba, Naoyuki; Takahashi, Ryo; Yamaguchi, Yuya
2015-01-01
There are a lot of works within a class of classically scale invariant model, which is motivated by solving the gauge hierarchy problem. In this context, the Higgs mass vanishes at the UV scale due to the classically scale invariance, and is generated via the Coleman-Weinberg mechanism. Since the mass generation should occur not so far from the electroweak scale, we extend the standard model only around the TeV scale. We construct a model which can achieve the gauge coupling unification at the UV scale. In the same way, the model can realize the vacuum stability, smallness of active neutrino masses, baryon asymmetry of the universe, and dark matter relic abundance. The model predicts the existence vector-like fermions charged under $SU(3)_C$ with masses lower than $1\\,{\\rm TeV}$, and the SM singlet Majorana dark matter with mass lower than $2.6\\,{\\rm TeV}$.
On the Galilean non-invariance of classical electromagnetism
Energy Technology Data Exchange (ETDEWEB)
Preti, Giovanni; De Felice, Fernando; Masiero, Luca [Dipartimento di Fisica ' Galileo Galilei' , Universita degli Studi di Padova (Italy)], E-mail: giovanni.preti@pd.infn.it, E-mail: fernando.defelice@pd.infn.it, E-mail: masieroluca@yahoo.it
2009-03-15
When asked to explain the Galilean non-invariance of classical electromagnetism on the basis of pre-relativistic considerations alone, students-and sometimes their teachers too-may face an impasse. Indeed, they often argue that a pre-relativistic physicist could most obviously have provided the explanation 'at a glance', on the basis of the presence of a parameter c with the dimensions of a velocity in Maxwell's equations, being well aware of the fact that any velocity is non-invariant in Galilean relativity. This 'obvious' answer, however popular, is not correct due to the actual observer-invariance of the Maxwell parameter c in pre-relativistic physics too. A pre-relativistic physicist would therefore have needed a different explanation. Playing the role of this physicist, we pedagogically show how a proof of the Galilean non-invariance of classical electromagnetism can be obtained, resting on simple pre-relativistic considerations alone.
Classical Loop Actions of Gauge Theories
Armand-Ugon, D; Griego, J R; Setaro, L; Armand-Ugon, Daniel; Gambini, Rodolfo; Griego, Jorge; Setaro, Leonardo
1994-01-01
Since the first attempts to quantize Gauge Theories and Gravity in the loop representation, the problem of the determination of the corresponding classical actions has been raised. Here we propose a general procedure to determine these actions and we explicitly apply it in the case of electromagnetism. Going to the lattice we show that the electromagnetic action in terms of loops is equivalent to the Wilson action, allowing to do Montecarlo calculations in a gauge invariant way. In the continuum these actions need to be regularized and they are the natural candidates to describe the theory in a ``confining phase''.
Diffeomorphism Invariant Theories and Vector Supersymmetry
Piguet, O
2000-01-01
Einstein gravity in the Palatini first order formalism is shown to possess a vector supersymmetry of the type encountered in the topological gauge theories. A peculiar feature of the gravitationel theory is the link of this vector supersymmetry with the field equation of motion of the Faddeev-Popov ghost associated to diffeomorphism invariance.
Classical glueballs in non-Abelian Born-Infeld theory
Galtsov, D V; Gal'tsov, Dmitri; Kerner, Richard
2000-01-01
It is shown that the Born-Infeld-type modification of the quadratic Yang-Mills action suggested by the superstring theory gives rise to classical particle-like solutions prohibited in the standard Yang-Mills theory. This becomes possible due to the scale invariance breaking by the Born-Infeld non-linearity. New classical glueballs are sphaleronic in nature and exhibit a striking similarity with the Bartnik-McKinnon solutions of the Yang-Mills theory coupled to gravity.
Classical Electromagnetic Theory
VanderLinde, Jack
2004-01-01
This book is a self contained course in electromagnetic theory suitable for senior physics and electrical engineering students as well as graduate students whose past has not prepared them well for books such as Jackson or Landau and Lifschitz. The text is liberally sprinkled with worked examples illustrating the application of the theory to various physical problems. In this new edition I have endeavored to improve the accuracy and readability, added and further clarified examples, added sections on Schwarz-Christoffel mappings, and to make the book more self sufficient added an appendix on orthogonal function expansions and added the derivation of Bessel functions and Legendre polynomials as well as derivation of their generating functions. The number of student exercises has been increased by 45 over the previous edition. This book stresses the unity of electromagnetic theory with electric and magnetic fields developed in parallel. SI units are used throughout and considerable use is made of tensor notatio...
On adiabatic invariant in generalized Galileon theories
Ema, Yohei; Mukaida, Kyohei; Nakayama, Kazunori
2015-01-01
We consider background dynamics of generalized Galileon theories in the context of inflation, where gravity and inflaton are non-minimally coupled to each other. In the inflaton oscillation regime, the Hubble parameter and energy density oscillate violently in many cases, in contrast to the Einstein gravity with minimally coupled inflaton. However, we find that there is an adiabatic invariant in the inflaton oscillation regime in any generalized Galileon theory. This adiabatic invariant is useful in estimating the expansion law of the universe and also the particle production rate due to the oscillation of the Hubble parameter.
Majorana dark matter in a classically scale invariant model
Benic, Sanjin
2014-01-01
We analyze a classically scale invariant extension of the Standard Model with dark gauge $U(1)_X$ broken by doubly charge scalar $\\Phi$ leaving a remnant $Z_2$ symmetry. Dark fermions are introduced as dark matter candidates and for anomaly reasons we introduce two chiral fermions. Due to classical scale invariance, bare mass term that would mix these two states is absent and they end up as stable Majorana fermions $N_1$ and $N_2$. We calculate cross sections for $N_aN_a \\to \\phi\\phi$, $N_aN_a \\to X^\\mu \\phi$ and $N_2N_2 \\to N_1N_1$ annihilation channels. We put constraints to the model from the Higgs searches at the LHC, dark matter relic abundance and dark matter direct detection limits by LUX. The dark gauge boson plays a crucial role in the Coleman-Weinberg mechanism and has to be heavier then 680 GeV. The viable mass region for dark matter is from 470 GeV up to a few TeV. In the case when two Majorana fermions have different masses, two dark matter signals at direct detection experiments could provide a ...
Suhov, Y.
We begin with the definition of information gained by knowing that an event A has occurred: iota (A) = -log_2 {{P}}(A). (A dual point of view is also useful (although more evasive), where iota (A) is the amount of information needed to specify event A.) Here and below {{P}} stands for the underlying probability distribution. So the rarer an event A, the more information we gain if we know it has occurred. (More broadly, the rarer an event A, the more impact it will have. For example, the unlikely event that occurred in 1938 when fishermen caught a coelacanth - a prehistoric fish believed to be extinct - required a significant change to beliefs about evolution and biology. On the other hand, the likely event of catching a herring or a tuna would hardly imply any change in theories.)
Classical theory of radiating strings
Copeland, Edmund J.; Haws, D.; Hindmarsh, M.
1990-01-01
The divergent part of the self force of a radiating string coupled to gravity, an antisymmetric tensor and a dilaton in four dimensions are calculated to first order in classical perturbation theory. While this divergence can be absorbed into a renormalization of the string tension, demanding that both it and the divergence in the energy momentum tensor vanish forces the string to have the couplings of compactified N = 1 D = 10 supergravity. In effect, supersymmetry cures the classical infinities.
Invariant functionals in higher-spin theory
Vasiliev, M. A.
2017-03-01
A new construction for gauge invariant functionals in the nonlinear higher-spin theory is proposed. Being supported by differential forms closed by virtue of the higher-spin equations, invariant functionals are associated with central elements of the higher-spin algebra. In the on-shell AdS4 higher-spin theory we identify a four-form conjectured to represent the generating functional for 3d boundary correlators and a two-form argued to support charges for black hole solutions. Two actions for 3d boundary conformal higher-spin theory are associated with the two parity-invariant higher-spin models in AdS4. The peculiarity of the spinorial formulation of the on-shell AdS3 higher-spin theory, where the invariant functional is supported by a two-form, is conjectured to be related to the holomorphic factorization at the boundary. The nonlinear part of the star-product function F* (B (x)) in the higher-spin equations is argued to lead to divergencies in the boundary limit representing singularities at coinciding boundary space-time points of the factors of B (x), which can be regularized by the point splitting. An interpretation of the RG flow in terms of proposed construction is briefly discussed.
Field redefinition invariance in quantum field theory
Apfeldorf, K M; Apfeldorf, Karyn M; Ordonez, Carlos
1994-01-01
We investigate the consequences of field redefinition invariance in quantum field theory by carefully performing nonlinear transformations in the path integral. We first present a ``paradox'' whereby a 1+1 freemassless scalar theory on a Minkowskian cylinder is reduced to an effectively quantum mechanical theory. We perform field redefinitions both before and after reduction to suggest that one should not ignore operator ordering issues in quantum field theory. We next employ a discretized version of the path integral for a free massless scalar quantum field in d dimensions to show that beyond the usual jacobian term, an infinite series of divergent ``extra'' terms arises in the action whenever a nonlinear field redefinition is made. The explicit forms for the first couple of these terms are derived. We evaluate Feynman diagrams to illustrate the importance of retaining the extra terms, and conjecture that these extra terms are the exact counterterms necessary to render physical quantities invariant under fie...
Spherical harmonics, invariant theory and Maxwell's poles
Dowker, J S
2008-01-01
I discuss the relation between harmonic polynomials and invariant theory and show that homogeneous, harmonic polynomials correspond to ternary forms that are apolar to a base conic (the absolute). The calculation of Schlesinger that replaces such a form by a polarised binary form is reviewed. It is suggested that Sylvester's theorem on the uniqueness of Maxwell's pole expression for harmonics is renamed the Clebsch-Sylvester theorem. The relation between certain constructs in invariant theory and angular momentum theory is enlarged upon and I resurrect the Joos--Weinberg matrices. Hilbert's projection operators are considered and their generalisations by Story and Elliott are related to similar, more recent constructions in group theory and quantum mechanics, the ternary case being equivalent to SU(3).
Ghost Equations and Diffeomorphism Invariant Theories
Piguet, O
2000-01-01
Four-dimensional Einstein gravity in the Palatini first order formalism is shown to possess a vector supersymmetry of the same type as found in the topological theories for Yang-Mills fields. A peculiar feature of the gravitational theory, characterized by diffeomorphism invariance, is a direct link of vector supersymmetry with the field equation of motion for the Faddeev-Popov ghost of diffeomorphisms.
Gauge invariant observables from Takahashi-Tanimoto scalar solutions in open string field theory
Zeze, Syoji
2014-01-01
Using Maccaferri's formula, we derive new wedge based solutions of open string field theory. The solutions are gauge equivalent to the Takahashi-Tanimoto scalar solutions. The classical action and the gauge invariant overlap are evaluated analytically. We find a perturbative vacuum solution whose gauge invariant observables vanish. We also identify a tachyon vacuum solution whose gauge invariant observables are identical to those of the Erler-Schnabl solution.
Classical and Quantum Theory of Perturbations in Inflationary Universe Models
Brandenberger, R H; Mukhanov, V
1993-01-01
A brief introduction to the gauge invariant classical and quantum theory of cosmological perturbations is given. The formalism is applied to inflationary Universe models and yields a consistent and unified description of the generation and evolution of fluctuations. A general formula for the amplitude of cosmological perturbations in inflationary cosmology is derived.
Invariant Set Theory and the Symbolism of Quantum Measurement
Palmer, T N
2015-01-01
Elements of a novel theory of quantum physics are developed, synthesising the role of symbolism in describing quantum measurement and in the topological representation of fractal invariant sets in nonlinear dynamical systems theory. In this synthesis, the universe $U$ is treated as an isolated deterministic dynamical system evolving precisely on a measure-zero fractal invariant subset $I_U$ of its state space. A non-classical approach to the physics of $U$ is developed by treating the geometry of $I_U$ as more primitive than dynamical evolution equations on $I_U$. A specific symbolic representation of $I_U$ is constructed which encodes quaternionic multiplication and from which the statistical properties of complex Hilbert Space vectors are emergent. The Hilbert Space itself arises as the singular limit of Invariant Set Theory as a fractal parameter $N \\rightarrow \\infty$. Although the Hilbert Space of quantum theory is counterfactually complete, the measure-zero set $I_U$ is counterfactually incomplete, no m...
Embedded graph invariants in Chern-Simons theory
Major, Seth A.
1998-01-01
Chern-Simons gauge theory, since its inception as a topological quantum field theory, has proved to be a rich source of understanding for knot invariants. In this work the theory is used to explore the definition of the expectation value of a network of Wilson lines - an embedded graph invariant. Using a slight generalization of the variational method, lowest-order results for invariants for arbitrary valence graphs are derived; gauge invariant operators are introduced; and some higher order ...
A new type of adiabatic invariants for nonconservative systems of generalized classical mechanics
Institute of Scientific and Technical Information of China (English)
Zhang Yi
2006-01-01
The perturbations to symmetries and adiabatic invariants for nonconservative systems of generalized classical mechanics are studied. The exact invariant in the form of Hojman from a particular Lie symmetry for an undisturbed system of generalized mechanics is given. Based on the concept of high-order adiabatic invariant in generalized mechanics, the perturbation to Lie symmetry for the system under the action of small disturbance is investigated, and a new adiabatic invariant for the nonconservative system of generalized classical mechanics is obtained, which can be called the Hojman adiabatic invariant. An example is also given to illustrate the application of the results.
Construction of exact complex dynamical invariant of a two-dimensional classical system
Indian Academy of Sciences (India)
Fakir Chand; S C Mishra
2006-12-01
We present the construction of exact complex dynamical invariant of a two-dimensional classical dynamical system on an extended complex space utilizing Lie algebraic approach. These invariants are expected to play a vital role in understanding the complex trajectories of both classical and quantum systems.
Translational invariance in nucleation theories: Theoretical formulation
Energy Technology Data Exchange (ETDEWEB)
Drossinos, Y.; Kevrekidis, P. G.; Georgopoulos, P. G.
2001-03-01
The consequences of spontaneously broken translational invariance on the nucleation-rate statistical prefactor in theories of first-order phase transitions are analyzed. A hybrid, semiphenomenological approach based on field-theoretic analyses of condensation and modern density-functional theories of nucleation is adopted to provide a unified prescription for the incorporation of translational-invariance corrections to nucleation-rate predictions. A connection between these theories is obtained starting from a quantum-mechanical Hamiltonian and using methods developed in the context of studies on Bose-Einstein condensation. An extremum principle is used to derive an integro-differential equation for the spatially nonuniform mean-field order-parameter profile; the appropriate order parameter becomes the square root of the fluid density. The importance of the attractive intermolecular potential is emphasized, whereas the repulsive two-body potential is approximated by considering hard-sphere collisions. The functional form of the degenerate translational eigenmodes in three dimensions is related to the mean-field order parameter, and their contribution to the nucleation-rate prefactor is evaluated. The solution of the Euler-Lagrange variational equation is discussed in terms of either a proposed variational trial function or the complete numerical solution of the associated boundary-value integro-differential problem. Alternatively, if the attractive potential is not explicitly known, an approach that allows its formal determination from its moments is presented.
Conformal invariance in quantum field theory
Todorov, Ivan T; Petkova, Valentina B
1978-01-01
The present volume is an extended and up-to-date version of two sets of lectures by the first author and it reviews more recent work. The notes aim to present a self-contained exposition of a constructive approach to conformal invariant quantum field theory. Other parts in application of the conformal group to quantum physics are only briefly mentioned. The relevant mathematical material (harmonic analysis on Euclidean conformal groups) is briefly summarized. A new exposition of physical applications is given, which includes an explicit construction of the vacuum operator product expansion for the free zero mass fields.
Invariant Regularization of Supersymmetric Chiral Gauge Theory
Suzuki, H
1999-01-01
We present a regularization scheme which respects the supersymmetry and the maximal background gauge covariance in supersymmetric chiral gauge theories. When the anomaly cancellation condition is satisfied, the effective action in the superfield background field method automatically restores the gauge invariance without counterterms. The scheme also provides a background gauge covariant definition of composite operators that is especially useful in analyzing anomalies. We present several applications: The minimal consistent gauge anomaly; the super-chiral anomaly and the superconformal anomaly; as the corresponding anomalous commutators, the Konishi anomaly and an anomalous supersymmetric transformation law of the supercurrent (the ``central extension'' of N=1 supersymmetry algebra) and of the R-current.
Origin of gauge invariance in string theory
Horowitz, G. T.; Strominger, A.
1986-01-01
A first quantization of the space-time embedding Chi exp mu and the world-sheet metric rho of the open bosonic string. The world-sheet metric rho decouples from S-matrix elements in 26 dimensions. This formulation of the theory naturally includes 26-dimensional gauge transformations. The gauge invariance of S-matrix elements is a direct consequence of the decoupling of rho. Second quantization leads to a string field Phi(Chi exp mu, rho) with a gauge-covariant equation of motion.
Conformal invariance and Hamilton Jacobi theory for dissipative systems
Kiehn, R. M.
1975-01-01
For certain dissipative systems, a comparison can be made between the Hamilton-Jacobi theory and the conformal invariance of action theory. The two concepts are not identical, but the conformal action theory covers the Hamilton-Jacobi theory.
Classically Scale Invariant Inflation, WIMPzilla, and (A)gravity
Farzinnia, Arsham
2015-01-01
We introduce a minimal and yet comprehensive framework with $CP$- and classical scale-symmetries, in order to simultaneously address the hierarchy problem, neutrino masses, dark matter, and inflation. One complex gauge singlet scalar and three flavors of the right-handed Majorana neutrinos are added to the standard model content, facilitating the see-saw mechanism, among others. An adimensional theory of gravity (Agravity) is employed as the UV-completion candidate, allowing for the trans-Planckian field excursions. The electroweak and the Planck scales are induced by the Higgs portal and the scalar non-minimal couplings, respectively, once a Coleman-Weinberg dynamically-generated vacuum expectation value for the singlet scalar is obtained. All scales are free of any mutual quadratic destabilization. The $CP$-symmetry prevents a decay of the pseudoscalar singlet, rendering it a suitable WIMPzilla dark matter candidate with the correct observational relic abundance. Identifying the pseudo-Nambu-Goldstone boson...
Norbury, John W.
1989-01-01
The invariance of classical electromagnetism under charge-conjugation, parity, and time-reversal (CPT) is studied by considering the motion of a charged particle in electric and magnetic fields. Upon applying CPT transformations to various physical quantities and noting that the motion still behaves physically demonstrates invariance.
Polyakov's spin factor for a classical spinning particle via BRST invariant path integral
Cho, J; Lee, H; Jin-Ho Cho; Seungjoon Hyun; Hyuk-Jae Lee
1994-01-01
For the "classical" formulation of a massive spinning particle, the propagator is obtained along with the spin factor. We treat the system with two kinds of constraints that were recently shown to be concerned with the reparametrization invariance and "quasi-supersymmetry". In the path integral, the BRST invariant Lagrangian is used and the same spin factor is obtained as in the pseudo-classical formulation.
Quantum chaotic scattering in graphene systems in the absence of invariant classical dynamics.
Wang, Guang-Lei; Ying, Lei; Lai, Ying-Cheng; Grebogi, Celso
2013-05-01
Quantum chaotic scattering is referred to as the study of quantum behaviors of open Hamiltonian systems that exhibit transient chaos in the classical limit. Traditionally a central issue in this field is how the elements of the scattering matrix or their functions fluctuate as a system parameter, e.g., the electron Fermi energy, is changed. A tacit hypothesis underlying previous works was that the underlying classical phase-space structure remains invariant as the parameter varies, so semiclassical theory can be used to explain various phenomena in quantum chaotic scattering. There are, however, experimental situations where the corresponding classical chaotic dynamics can change characteristically with some physical parameter. Multiple-terminal quantum dots are one such example where, when a magnetic field is present, the classical chaotic-scattering dynamics can change between being nonhyperbolic and being hyperbolic as the Fermi energy is changed continuously. For such systems semiclassical theory is inadequate to account for the characteristics of conductance fluctuations with the Fermi energy. To develop a general framework for quantum chaotic scattering associated with variable classical dynamics, we use multi-terminal graphene quantum-dot systems as a prototypical model. We find that significant conductance fluctuations occur with the Fermi energy even for fixed magnetic field strength, and the characteristics of the fluctuation patterns depend on the energy. We propose and validate that the statistical behaviors of the conductance-fluctuation patterns can be understood by the complex eigenvalue spectrum of the generalized, complex Hamiltonian of the system which includes self-energies resulted from the interactions between the device and the semi-infinite leads. As the Fermi energy is increased, complex eigenvalues with extremely smaller imaginary parts emerge, leading to sharp resonances in the conductance.
C, P, and T invariance of noncommutative gauge theories
Sheikh-Jabbari
2000-06-05
In this paper we study the invariance of the noncommutative gauge theories under C, P, and T transformations. For the noncommutative space (when only the spatial part of straight theta is nonzero) we show that noncommutative QED (NCQED) is parity invariant. In addition, we show that under charge conjugation the theory on noncommutative R(4)(straight theta) is transformed to the theory on R(4)(-straight theta), so NCQED is a CP violating theory. The theory remains invariant under time reversal if, together with proper changes in fields, we also change straight theta by -straight theta. Hence altogether NCQED is CPT invariant. Moreover, we show that the CPT invariance holds for general noncommutative space-time.
Second invariant for two-dimensional classical super systems
Indian Academy of Sciences (India)
S C Mishra; Roshan Lal; Veena Mishra
2003-10-01
Construction of superpotentials for two-dimensional classical super systems (for ≥ 2) is carried out. Some interesting potentials have been studied in their super form and also their integrability.
The Topological Theory of the Milnor Invariant $\\bar{\\mu}(1,2,3)$
Leal, Lorenzo
2007-01-01
We study a topological Abelian gauge theory that generalizes the Abelian Chern-Simons one, and that leads in a natural way to the Milnor's link invariant $\\bar{\\mu}(1,2,3)$ when the classical action on-shell is calculated.
The Kubelka-Munk Theory for Color Image Invariant Properties
Geusebroek, J.M.; Gevers, Th.; Smeulders, A.W.M.
2002-01-01
A fundamental problem in color image processing is the integration of the physical laws of light reflection into image processing results, the probem known as photometric invariance. The derivation of object properties from color images yields the extraction of geometric and photometric invariants from color images. Photometric invariance is to be derived from the physics of refelection. In this paper, we rehearse the results from radiative transfer theory to model the reflection and transmis...
The Chern-Simons invariant as the natural time variable for classical and quantum cosmology
Smolin, L; Smolin, Lee; Soo, Chopin
1995-01-01
We propose that the Chern-Simons invariant of the Ashtekar-Sen connection is the natural internal time coordinate for classical and quantum cosmology. The reasons for this are a number of interesting properties of this functional, which we describe here. 1)It is a function on the gauge and diffeomorphism invariant configuration space, whose gradient is orthogonal to the two physical degrees of freedom, in the metric defined by the Ashtekar formulation of general relativity. 2)The imaginary part of the Chern-Simons form reduces in the limit of small cosmological constant, \\Lambda, and solutions close to DeSitter spacetime, to the York extrinsic time coordinate. 3)Small matter-field excitations of the Chern-Simons state satisfy, by virtue of the quantum constraints, a functional Schroedinger equation in which the matter fields evolve on a DeSitter background in the Chern-Simons time. We then n propose this is the natural vacuum state of the theory for \\Lambda \
Invariant regularization of anomaly-free chiral theories
Chang, L N; Chang, Lay Nam; Soo, Chopin
1997-01-01
We present a generalization of the Frolov-Slavnov invariant regularization scheme for chiral fermion theories in curved spacetimes. The Lagrangian level regularization is explicitly invariant under all the local gauge symmetries of the theory, including local Lorentz invariance. The perturbative scheme works for {\\it arbitrary} representations which satisfy the chiral gauge anomaly and mixed Lorentz-gauge anomaly cancellation conditions. Anomalous theories on the other hand manifest themselves by having divergent fermion loops which remain unregularized by the scheme. Since the invariant scheme is promoted to also include local Lorentz invariance, spectator fields which do not couple to gravity cannot be, and are not, introduced. Furthermore, the scheme is truly Weyl(chiral) in that {\\it all} fields, including the regulators, are left-handed; and {\\it only the left-handed spin connection} is needed. The scheme is therefore well-suited for the perturbative study of all four known forces in a completely chiral ...
Modular invariants and fusion rule automorphisms from Galois theory
Fuchs, J; Schellekens, Adrian Norbert; Schweigert, C; Beatriz Gato-Rivera; Bert Schellekens; Christoph Schweigert
1994-01-01
We show that Galois theory of cyclotomic number fields provides a powerful tool to construct systematically integer-valued matrices commuting with the modular matrix S, as well as automorphisms of the fusion rules. Both of these prescriptions allow the construction of modular invariants and offer new insight in the structure of known exceptional invariants.
Measurement Invariance: A Foundational Principle for Quantitative Theory Building
Nimon, Kim; Reio, Thomas G., Jr.
2011-01-01
This article describes why measurement invariance is a critical issue to quantitative theory building within the field of human resource development. Readers will learn what measurement invariance is and how to test for its presence using techniques that are accessible to applied researchers. Using data from a LibQUAL+[TM] study of user…
Scaling theory of {{{Z}}_{2}} topological invariants
Chen, Wei; Sigrist, Manfred; Schnyder, Andreas P.
2016-09-01
For inversion-symmetric topological insulators and superconductors characterized by {{{Z}}2} topological invariants, two scaling schemes are proposed to judge topological phase transitions driven by an energy parameter. The scaling schemes renormalize either the phase gradient or the second derivative of the Pfaffian of the time-reversal operator, through which the renormalization group flow of the driving energy parameter can be obtained. The Pfaffian near the time-reversal invariant momentum is revealed to display a universal critical behavior for a great variety of models examined.
Equilibration properties of classical integrable field theories
De Luca, Andrea; Mussardo, Giuseppe
2016-06-01
We study the equilibration properties of classical integrable field theories at a finite energy density, with a time evolution that starts from initial conditions far from equilibrium. These classical field theories may be regarded as quantum field theories in the regime of high occupation numbers. This observation permits to recover the classical quantities from the quantum ones by taking a proper \\hslash \\to 0 limit. In particular, the time averages of the classical theories can be expressed in terms of a suitable version of the LeClair-Mussardo formula relative to the generalized Gibbs ensemble. For the purposes of handling time averages, our approach provides a solution of the problem of the infinite gap solutions of the inverse scattering method.
Classical theory of electric and magnetic fields
Good, Roland H
1971-01-01
Classical Theory of Electric and Magnetic Fields is a textbook on the principles of electricity and magnetism. This book discusses mathematical techniques, calculations, with examples of physical reasoning, that are generally applied in theoretical physics. This text reviews the classical theory of electric and magnetic fields, Maxwell's Equations, Lorentz Force, and Faraday's Law of Induction. The book also focuses on electrostatics and the general methods for solving electrostatic problems concerning images, inversion, complex variable, or separation of variables. The text also explains ma
Noncommutative field theory and violation of translation invariance
Bertolami, O
2003-01-01
Noncommutative field theories with commutator of the coordinates of the form $[x^{mu},x^{nu}]=i Lambda_{quad omega}^{mu nu}x^{omega}$ are studied. Explicit Lorentz invariance is mantained considering $Lambda $ a Lorentz tensor. It is shown that a free quantum field theory is not affected. Since invariance under translations is broken, the conservation of energy-momentum is violated, obeying a new law which is expressed by a Poincar'e-invariant equation. The resulting new kinematics is studied and applied to simple examples and to astrophysical puzzles, such as the observed violation of the GZK cutoff. The $lambda
Quantum theory is classical mechanics with non-local existence
Hegseth, John
2009-01-01
I propose a new and direct connection between classical mechanics and quantum mechanics where I derive the quantum mechanical propagator from a variational principle. This variational principle is Hamilton's modified principle generalized to allow many paths due to the non-local existence of particles in phase space. This principle allows a physical system to evolve non-locally in phase space while still allowing a representation that uses many classical paths. Whereas a point in phase space represents a classical system's state, I represent the state of a non-local system by a mixed trajectory. This formulation naturally leads to the transactional interpretation for resolving the paradoxes of the measurement problem. This principle also suggests a more flexible framework for formulating theories based on invariant actions and provides a single conceptual framework for discussing many areas of science.
A Classical Introduction to Galois Theory
Newman, Stephen C
2012-01-01
This book provides an introduction to Galois theory and focuses on one central theme - the solvability of polynomials by radicals. Both classical and modern approaches to the subject are described in turn in order to have the former (which is relatively concrete and computational) provide motivation for the latter (which can be quite abstract). The theme of the book is historically the reason that Galois theory was created, and it continues to provide a platform for exploring both classical and modern concepts. This book examines a number of problems arising in the area of classical mathematic
Perturbative quantization of Yang-Mills theory with classical double as gauge algebra
Ruiz, F Ruiz
2015-01-01
Perturbative quantization of Yang-Mills theory with a gauge algebra given by the classical double of a semisimple Lie algebra is considered. The classical double of a real Lie algebra is a nonsemisimple real Lie algebra that admits a nonpositive definite invariant metric, the indefiniteness of the metric suggesting an apparent lack of unitarity. It is shown that the theory is UV divergent at one loop and that there are no radiative corrections at higher loops. One-loop UV divergences are removed through renormalization of the coupling constant, thus introducing a renormalization scale. The terms in the classical action that would spoil unitarity are proved to be cohomologically trivial with respect to the Slavnov-Taylor operator that controls gauge invariance for the quantum theory. Hence they do not contribute gauge invariant radiative corrections to the quantum effective action and the theory is unitary.
Perturbative quantization of Yang-Mills theory with classical double as gauge algebra
Energy Technology Data Exchange (ETDEWEB)
Ruiz Ruiz, F. [Universidad Complutense de Madrid, Departamento de Fisica Teorica I, Madrid (Spain)
2016-02-15
Perturbative quantization of Yang-Mills theory with a gauge algebra given by the classical double of a semisimple Lie algebra is considered. The classical double of a real Lie algebra is a nonsemisimple real Lie algebra that admits a nonpositive definite invariant metric, the indefiniteness of the metric suggesting an apparent lack of unitarity. It is shown that the theory is UV divergent at one loop and that there are no radiative corrections at higher loops. One-loop UV divergences are removed through renormalization of the coupling constant, thus introducing a renormalization scale. The terms in the classical action that would spoil unitarity are proved to be cohomologically trivial with respect to the Slavnov-Taylor operator that controls gauge invariance for the quantum theory. Hence they do not contribute gauge invariant radiative corrections to the quantum effective action and the theory is unitary. (orig.)
Generalizability Theory and Classical Test Theory
Brennan, Robert L.
2011-01-01
Broadly conceived, reliability involves quantifying the consistencies and inconsistencies in observed scores. Generalizability theory, or G theory, is particularly well suited to addressing such matters in that it enables an investigator to quantify and distinguish the sources of inconsistencies in observed scores that arise, or could arise, over…
Classical Theory, Postmodernism, and the Sociology Liberal Arts Curriculum.
Lembcke, Jerry Lee
1993-01-01
Discusses classical theory as a modernist endeavor to apprehend the phenomenon of "unity of disunity." Presents three ways that classical theory approaches the philosophy views of Durkheim, Marx, and Weber. Concludes that postmodernism validates the relevancy of classical theory. (CFR)
Unified classical path theories of pressure broadening.
Bottcher, C.
1971-01-01
Derivation of a unified classical path theory of pressure broadening, using only elementary concepts. It is shown that the theory of Smith, Cooper and Vidal (1969) is only correct at all frequencies to first order in the number density of perturbers.
Beam structures classical and advanced theories
Carrera, Erasmo; Petrolo, Marco
2011-01-01
Beam theories are exploited worldwide to analyze civil, mechanical, automotive, and aerospace structures. Many beam approaches have been proposed during the last centuries by eminent scientists such as Euler, Bernoulli, Navier, Timoshenko, Vlasov, etc. Most of these models are problem dependent: they provide reliable results for a given problem, for instance a given section and cannot be applied to a different one. Beam Structures: Classical and Advanced Theories proposes a new original unified approach to beam theory that includes practically all classical and advanced models for be
Prototype Theory and Classical Theory:An Explanation and Comparison
Institute of Scientific and Technical Information of China (English)
刘莹
2014-01-01
This paper discusses two different ways to understand categorization, which are classical theory and prototype theory. There is a deep exploration on how to understand categories, and different theoretical backgrounds of the two categorization the⁃ories. Furthermore, it reviews the limitations and advantages of both theories. And the comparison of the theories gives a clearer angle to understand their similarities and differences.
Invariant quantities in the scalar-tensor theories of gravitation
Jarv, Laur; Saal, Margus; Vilson, Ott
2014-01-01
We consider the general scalar-tensor gravity without derivative couplings. By rescaling of the metric and reparametrization of the scalar field, the theory can be presented in different conformal frames and parametrizations. In this work we argue, that while due to the freedom to transform the metric and the scalar field, the scalar field itself does not carry a physical meaning (in a generic parametrization), there are functions of the scalar field and its derivatives which remain invariant under the transformations. We put forward a scheme how to construct these invariants, discuss how to formulate the theory in terms of the invariants, and show how the observables like parametrized post-Newtonian parameters and characteristics of the cosmological solutions can be neatly expressed in terms of the invariants. In particular, we describe the scalar field solutions in Friedmann-Lema\\^itre-Robertson-Walker cosmology in Einstein and Jordan frames, and explain their correspondence despite the approximate equation...
Noncommutative Field Theory With General Translation Invariant Star Products
Rivera, Manolo
2015-01-01
We compute the two-point and four-point Green's function of the noncommutative $\\phi^{4}$ field theory; first with the s-ordered star products and then with a general translation invariant star product. We derive the differential expression for any translation invariant star product, and with the help of this expression we show that any of these products can be written in terms of a twist. Finally, using the notion of the twisted action of the infinitesimal Poincar\\'e transformations, we show that the commutator between the coordinate functions is invariant under Poincar\\'e transformations at a deformed level.
Vassiliev invariants; 1, braid groups and rational homotopy theory
Funar, L
1995-01-01
We get a detailed account of Vassiliev type invariants starting with Chen's theory of iterated integrals and Malcev's completion of discrete groups. The canonical injection of the group of pure braids into its completion is identified with the universal Kontsevich-Vassiliev invariant.Further we discuss the extension of this morphism to the whole braid group and the multiplication law for the last one.
Classical Ergodicity and Modern Portfolio Theory
Directory of Open Access Journals (Sweden)
Geoffrey Poitras
2015-01-01
Full Text Available What role have theoretical methods initially developed in mathematics and physics played in the progress of financial economics? What is the relationship between financial economics and econophysics? What is the relevance of the “classical ergodicity hypothesis” to modern portfolio theory? This paper addresses these questions by reviewing the etymology and history of the classical ergodicity hypothesis in 19th century statistical mechanics. An explanation of classical ergodicity is provided that establishes a connection to the fundamental empirical problem of using nonexperimental data to verify theoretical propositions in modern portfolio theory. The role of the ergodicity assumption in the ex post/ex ante quandary confronting modern portfolio theory is also examined.
Embedding inflation into the Standard Model - more evidence for classical scale invariance
Kannike, Kristjan; Raidal, Martti
2014-01-01
If cosmological inflation is due to a slowly rolling single inflation field taking trans-Planckian values as suggested by the BICEP2 measurement of primordial tensor modes in CMB, embedding inflation into the Standard Model challenges standard paradigm of effective field theories. Together with an apparent absence of Planck scale contributions to the Higgs mass and to the cosmological constant, BICEP2 provides further experimental evidence for the absence of large $M_{\\rm P}$ induced operators. We show that classical scale invariance, the paradigm that all fundamental scales in Nature are induced by quantum effects, solves the problem and allows for a remarkably simple scale-free Standard Model extension with inflaton without extending the gauge group. Due to trans-Planckian inflaton values and vevs, a dynamically induced Coleman-Weinberg-type inflaton potential of the model can predict tensor-to-scalar ratio $r$ in a large range, converging around the prediction of chaotic $m^2\\phi^2$ inflation for a large t...
Embedded graph invariants in Chern-Simons theory
Major, Seth A.
1999-06-01
Chern-Simons gauge theory, since its inception as a topological quantum field theory, has proved to be a rich source of understanding for knot invariants. In this work the theory is used to explore the definition of the expectation value of a network of Wilson lines — an embedded graph invariant. Using a generalization of the variational method, lowest-order results for invariants for graphs of arbitrary valence and general vertex tangent space structure are derived. Gauge invariant operators are introduced. Higher order results are found. The method used here provides a Vassiliev-type definition of graph invariants which depend on both the embedding of the graph and the group structure of the gauge theory. It is found that one need not frame individual vertices. However, without a global projection of the graph there is an ambiguity in the relation of the decomposition of distinct vertices. It is suggested that framing may be seen as arising from this ambiguity — as a way of relating frames at distinct vertices.
Embedded graph invariants in Chern-Simons theory
Major, S A
1999-01-01
Chern-Simons gauge theory, since its inception as a topological quantum field theory, has proved to be a rich source of understanding for knot invariants. In this work the theory is used to explore the definition of the expectation value of a network of Wilson lines - an embedded graph invariant. Using a slight generalization of the variational method, lowest-order results for invariants for arbitrary valence graphs are derived; gauge invariant operators are introduced; and some higher order results are found. The method used here provides a Vassiliev-type definition of graph invariants which depend on both the embedding of the graph and the group structure of the gauge theory. It is found that one need not frame individual vertices. Though, without a global projection of the graph, there is an ambiguity in the relation of the decomposition of distinct vertices. It is suggested that framing may be seen as arising from this ambiguity - as a way of relating frames at distinct vertices.
Classical theory of the hydrogen atom
Rashkovskiy, Sergey
2016-01-01
It is shown that all of the basic properties of the hydrogen atom can be consistently described in terms of classical electrodynamics instead of taking the electron to be a particle; we consider an electrically charged classical wave field, an "electron wave", which is held in a limited region of space by the electrostatic field of the proton. It is shown that quantum mechanics must be considered to be not a theory of particles but a classical field theory in the spirit of classical electrodynamics. In this case, we are not faced with difficulties in interpreting the results of the theory. In the framework of classical electrodynamics, all of the well-known regularities of the spontaneous emission of the hydrogen atom are obtained, which is usually derived in the framework of quantum electrodynamics. It is shown that there are no discrete states and discrete energy levels of the atom: the energy of the atom and its states change continuously. An explanation of the conventional corpuscular-statistical interpre...
Gauge Invariants and Correlators in Flavoured Quiver Gauge Theories
Mattioli, Paolo
2016-01-01
In this paper we study the construction of holomorphic gauge invariant operators for general quiver gauge theories with flavour symmetries. Using a characterisation of the gauge invariants in terms of equivalence classes generated by permutation actions, along with representation theory results in symmetric groups and unitary groups, we give a diagonal basis for the 2-point functions of holomorphic and anti-holomorphic operators. This involves a generalisation of the previously constructed Quiver Restricted Schur operators to the flavoured case. The 3-point functions are derived and shown to be given in terms of networks of symmetric group branching coefficients. The networks are constructed through cutting and gluing operations on the quivers.
Classical geometry from the quantum Liouville theory
Hadasz, L; Piatek, M; Hadasz, Leszek; Jaskolski, Zbigniew; Piatek, Marcin
2005-01-01
Zamolodchikov's recursion relations are used to analyze the existence and approximations to the classical conformal block in the case of four parabolic weights. Strong numerical evidence is found that the saddle point momenta arising in the classical limit of the DOZZ quantum Liouville theory are simply related to the geodesic length functions of the hyperbolic geometry on the 4-punctured Riemann sphere. Such relation provides new powerful methods for both numerical and analytical calculations of these functions. The consistency conditions for the factorization of the 4-point classical Liouville action in different channels are numerically verified. The factorization yields efficient numerical methods to calculate the 4-point classical action and, by the Polyakov conjecture, the accessory parameters of the Fuchsian uniformization of the 4-punctured sphere.
Classical geometry from the quantum Liouville theory
Energy Technology Data Exchange (ETDEWEB)
Hadasz, Leszek [M. Smoluchowski Institute of Physics, Jagellonian University, Reymonta 4, 30-059 Cracow (Poland)]. E-mail: hadasz@th.if.uj.edu.pl; Jaskolski, Zbigniew [Institute of Theoretical Physics, University of WrocIaw, pl. M. Borna, 950-204 WrocIaw (Poland)]. E-mail: jask@ift.uni.wroc.pl; Piatek, Marcin [Institute of Theoretical Physics, University of WrocIaw, pl. M. Borna, 950-204 WrocIaw (Poland)]. E-mail: piatek@ift.uni.wroc.pl
2005-09-26
Zamolodchikov's recursion relations are used to analyze the existence and approximations to the classical conformal block in the case of four parabolic weights. Strong numerical evidence is found that the saddle point momenta arising in the classical limit of the DOZZ quantum Liouville theory are simply related to the geodesic length functions of the hyperbolic geometry on the 4-punctured Riemann sphere. Such relation provides new powerful methods for both numerical and analytical calculations of these functions. The consistency conditions for the factorization of the 4-point classical Liouville action in different channels are numerically verified. The factorization yields efficient numerical methods to calculate the 4-point classical action and, by the Polyakov conjecture, the accessory parameters of the Fuchsian uniformization of the 4-punctured sphere.
"Scars" connect classical and quantum theory
Monteiro, T
1990-01-01
Chaotic systems are unstable and extremely sensitive to initial condititions. So far, scientists have been unable to demonstrate that the same kind of behaviour exists in quantum or microscopic systems. New connections have been discovered though between classical and quantum theory. One is the phenomena of 'scars' which cut through the wave function of a particle (1 page).
The classical theory of fields electromagnetism
Helrich, Carl S
2012-01-01
The study of classical electromagnetic fields is an adventure. The theory is complete mathematically and we are able to present it as an example of classical Newtonian experimental and mathematical philosophy. There is a set of foundational experiments, on which most of the theory is constructed. And then there is the bold theoretical proposal of a field-field interaction from James Clerk Maxwell. This textbook presents the theory of classical fields as a mathematical structure based solidly on laboratory experiments. Here the student is introduced to the beauty of classical field theory as a gem of theoretical physics. To keep the discussion fluid, the history is placed in a beginning chapter and some of the mathematical proofs in the appendices. Chapters on Green’s Functions and Laplace’s Equation and a discussion of Faraday’s Experiment further deepen the understanding. The chapter on Einstein’s relativity is an integral necessity to the text. Finally, chapters on particle motion and waves in a dis...
Direct detection of singlet dark matter in classically scale-invariant standard model
Directory of Open Access Journals (Sweden)
Kazuhiro Endo
2015-10-01
Full Text Available Classical scale invariance is one of the possible solutions to explain the origin of the electroweak scale. The simplest extension is the classically scale-invariant standard model augmented by a multiplet of gauge singlet real scalar. In the previous study it was shown that the properties of the Higgs potential deviate substantially, which can be observed in the International Linear Collider. On the other hand, since the multiplet does not acquire vacuum expectation value, the singlet components are stable and can be dark matter. In this letter we study the detectability of the real singlet scalar bosons in the experiment of the direct detection of dark matter. It is shown that a part of this model has already been excluded and the rest of the parameter space is within the reach of the future experiment.
Toward U(N|M) knot invariant from ABJM theory
Eynard, Bertrand; Kimura, Taro
2017-02-01
We study U(N|M) character expectation value with the supermatrix Chern-Simons theory, known as the ABJM matrix model, with emphasis on its connection to the knot invariant. This average just gives the half-BPS circular Wilson loop expectation value in ABJM theory, which shall correspond to the unknot invariant. We derive the determinantal formula, which gives U(N|M) character expectation values in terms of U(1|1) averages for a particular type of character representations. This means that the U(1|1) character expectation value is a building block for the U(N|M) averages and also, by an appropriate limit, for the U(N) invariants. In addition to the original model, we introduce another supermatrix model obtained through the symplectic transform, which is motivated by the torus knot Chern-Simons matrix model. We obtain the Rosso-Jones-type formula and the spectral curve for this case.
Towards U(N|M) knot invariant from ABJM theory
Eynard, Bertrand
2014-01-01
We study U(N|M) character expectation value with the supermatrix Chern-Simons theory, known as the ABJM matrix model, with emphasis on its connection to the knot invariant. This average just gives the half BPS circular Wilson loop expectation value in ABJM theory, which shall correspond to the unknot invariant. We derive the determinantal formula, which gives U(N|M) character expectation values in terms of U(1|1) averages for a particular type of character representations. This means that the U(1|1) character expectation value is a building block for all the U(N|M) averages, and in particular, by an appropriate limit, for the U(N) invariants. In addition to the original model, we introduce another supermatrix model obtained through the symplectic transform, which is motivated by the torus knot Chern-Simons matrix model. We obtain the Rosso-Jones-type formula and the spectral curve for this case.
Invariance, symmetry and periodicity in gauge theories
Energy Technology Data Exchange (ETDEWEB)
Jackiw, R
1980-02-01
The interplay between gauge transformations and coordinate transformations is discussed; the theory will aid in understanding the mixing of space-time and internal degrees of freedom. The subject is presented under the following headings: coordinate transformation laws for arbitrary fields, coordinate transformation laws for gauge fields, properties of symmetric gauge fields, construction of symmetric gauge fields, physical significance of gauge transformations, and magnetic monopole topology without Higgs fields. The paper ends with conclusions and suggestions for further research. (RWR)
Chern-Simons invariants on hyperbolic manifolds and topological quantum field theories
Energy Technology Data Exchange (ETDEWEB)
Bonora, L. [International School for Advanced Studies (SISSA/ISAS), Trieste (Italy); INFN, Sezione di Trieste (Italy); Bytsenko, A.A.; Goncalves, A.E. [Universidade Estadual de Londrina, Departamento de Fisica, Londrina-Parana (Brazil)
2016-11-15
We derive formulas for the classical Chern-Simons invariant of irreducible SU(n)-flat connections on negatively curved locally symmetric three-manifolds. We determine the condition for which the theory remains consistent (with basic physical principles). We show that a connection between holomorphic values of Selberg-type functions at point zero, associated with R-torsion of the flat bundle, and twisted Dirac operators acting on negatively curved manifolds, can be interpreted by means of the Chern-Simons invariant. On the basis of the Labastida-Marino-Ooguri-Vafa conjecture we analyze a representation of the Chern-Simons quantum partition function (as a generating series of quantum group invariants) in the form of an infinite product weighted by S-functions and Selberg-type functions. We consider the case of links and a knot and use the Rogers approach to discover certain symmetry and modular form identities. (orig.)
Chern-Simons Invariants on Hyperbolic Manifolds and Topological Quantum Field Theories
Bonora, Loriano; Goncalves, Antonio E
2016-01-01
We derive formulas for the classical Chern-Simons invariant of irreducible $SU(n)$-flat connections on negatively curved locally symmetric three-manifolds. We determine the condition for which the theory remains consistent (with basic physical principles). We show that a connection between holomorphic values of Selberg-type functions at point zero, associated with R-torsion of the flat bundle, and twisted Dirac operators acting on negatively curved manifolds, can be interpreted by means of the Chern-Simons invariant. On the basis of Labastida-Marino-Ooguri-Vafa conjecture we analyze a representation of the Chern-Simons quantum partition function (as a generating series of quantum group invariants) in the form of an infinite product weighted by S-functions and Selberg-type functions. We consider the case of links and a knot and use the Rogers approach to discover certain symmetry and modular form identities.
Renormalization of a Lorentz invariant doubled worldsheet theory
Nibbelink, Stefan Groot; Patalong, Peter
2013-01-01
Manifestly T-duality covariant worldsheet string models can be constructed by doubling the coordinate fields. We describe the underlying gauge symmetry of a recently proposed Lorentz invariant doubled worldsheet theory that makes half of the worldsheet degrees of freedom redundant. By shifting the Lagrange multiplier, that enforces the gauge fixing condition, the worldsheet action can be cast into various guises. We investigate the renormalization of this theory using a non-linear background/quantum split by employing a normal coordinate expansion adapted to the gauge-fixed theory. The propagator of the doubled coordinates contains a projection operator encoding that half of them do not propagate. We determine the doubled target space equations of motion by requiring one-loop Weyl invariance. Some of them are generalizations of the conventional sigma model beta-functions, while others seem to be novel to the doubled theory: In particular, a dilaton equation seems related to the strong constraint of double fie...
Quantum field theory from classical statistics
Wetterich, C
2011-01-01
An Ising-type classical statistical model is shown to describe quantum fermions. For a suitable time-evolution law for the probability distribution of the Ising-spins our model describes a quantum field theory for Dirac spinors in external electromagnetic fields, corresponding to a mean field approximation to quantum electrodynamics. All quantum features for the motion of an arbitrary number of electrons and positrons, including the characteristic interference effects for two-fermion states, are described by the classical statistical model. For one-particle states in the non-relativistic approximation we derive the Schr\\"odinger equation for a particle in a potential from the time evolution law for the probability distribution of the Ising-spins. Thus all characteristic quantum features, as interference in a double slit experiment, tunneling or discrete energy levels for stationary states, are derived from a classical statistical ensemble. Concerning the particle-wave-duality of quantum mechanics, the discret...
Form Invariance, Topological Fluctuations and Mass Gap of Yang-Mills Theory
Qian, Yachao
2016-01-01
In order to have a new perspective on the long-standing problem of the mass gap in Yang-Mills theory, we study the quantum Yang-Mills theory in the presence of topologically nontrivial backgrounds in this paper. The topologically stable gauge fields are constrained by the form invariance condition and the topological properties. Obeying these constraints, the known classical solutions to the Yang-Mills equation in the 3- and 4-dimensional Euclidean spaces are recovered, and the other allowed configurations form the nontrivial topological fluctuations at quantum level. Together, they constitute the background configurations, upon which the quantum Yang-Mills theory can be constructed. We demonstrate that the theory mimics the Higgs mechanism in a certain limit and develops a mass gap at semi-classical level on a flat space with finite size or on a sphere.
Curvaton reheating in a Scale Invariant Two Measures Theory
Guendelman, Eduardo I
2015-01-01
The curvaton reheating mechanism in a Scale Invariant Two Measures Theory defined in terms of two independent non-Riemannian volume forms (alternative generally covariant integration measure densities) on the space-time manifold which are metric independent is studied. The model involves two scalar matter fields, a dilaton, that transforms under scale transformations and it will be used also as the inflaton of the model and another scalar, which does not transform under scale transformations and which will play the role of a curvaton field. Potentials of appropriate form so that the pertinent action is invariant under global Weyl-scale symmetry are introduced. Scale invariance is spontaneously broken upon integration of the equations of motion. After performing transition to the physical Einstein frame we obtain: (i) For given value of the curvaton field an effective potential for the scalar field with two flat regions for the dilaton which allows for a unified description of both early universe inflation as ...
A new dynamics of electroweak symmetry breaking with classically scale invariance
Haba, Naoyuki; Kitazawa, Noriaki; Yamaguchi, Yuya
2015-01-01
We propose a new dynamics of the electroweak symmetry breaking in a classically scale invariant version of the standard model. The scale invariance is broken by the condensations of additional fermions under a strong coupling dynamics. The electroweak symmetry breaking is triggered by negative mass squared of the elementary Higgs doublet, which is dynamically generated through the bosonic seesaw mechanism. We introduce a real pseudo-scalar singlet field interacting with additional fermions and Higgs doublet in order to avoid massless Nambu-Goldstone bosons from the chiral symmetry breaking in a strong coupling sector. We investigate the mass spectra and decay rates of these pseudo-Nambu-Goldstone bosons, and show they can decay fast enough without cosmological problems. We further evaluate the energy dependences of the couplings between elementary fields perturbatively, and find that our model is the first one which realizes the flatland scenario with the dimensional transmutation by the strong coupling dynam...
A new dynamics of electroweak symmetry breaking with classically scale invariance
Directory of Open Access Journals (Sweden)
Naoyuki Haba
2016-04-01
Full Text Available We propose a new dynamics of the electroweak symmetry breaking in a classically scale invariant version of the standard model. The scale invariance is broken by the condensations of additional fermions under a strong coupling dynamics. The electroweak symmetry breaking is triggered by negative mass squared of the elementary Higgs doublet, which is dynamically generated through the bosonic seesaw mechanism. We introduce a real pseudo-scalar singlet field interacting with additional fermions and Higgs doublet in order to avoid massless Nambu–Goldstone bosons from the chiral symmetry breaking in a strong coupling sector. We investigate the mass spectra and decay rates of these pseudo-Nambu–Goldstone bosons, and show they can decay fast enough without cosmological problems. We further show that our model can make the electroweak vacuum stable.
Ultraviolet singularities in classical brane theory
Lechner, Kurt
2010-01-01
We construct for the first time an energy-momentum tensor for the electromagnetic field of a p-brane in arbitrary dimensions, entailing finite energy-momentum integrals. The construction relies on distribution theory and is based on a Lorentz-invariant regularization, followed by the subtraction of divergent and finite counterterms supported on the brane. The resulting energy-momentum tensor turns out to be uniquely determined. We perform the construction explicitly for a generic stationary brane. For a brane in arbitrary motion our approach provides a new paradigm for the derivation of the, otherwise divergent, self-force of the brane. The so derived self-force is automatically finite and guarantees, by construction, energy-momentum conservation.
[Taxonomic theory for non-classical systematics].
Pavlinov, I Ia
2012-01-01
Outlined briefly are basic principles of construing general taxonomic theory for biological systematics considered in the context of non-classical scientific paradigm. The necessity of such kind of theory is substantiated, and some key points of its elaboration are exposed: its interpretation as a framework concept for the partial taxonomic theories in various schools of systematics; elaboration of idea of cognitive situation including three interrelated components, namely subject, object, and epistemic ones; its construing as a content-wisely interpreted quasi-axiomatics, with strong structuring of its conceptual space including demarcation between axioms and inferring rules; its construing as a "conceptual pyramid" of concepts of various levels of generality; inclusion of a basic model into definition of the taxonomic system (classification) regulating its content. Two problems are indicated as fundamental: definition of taxonomic diversity as a subject domain for the systematics as a whole; definition of onto-epistemological status of taxonomic system (classification) in general and of taxa in particular.
String organization of field theories duality and gauge invariance
Feng, Y J; Feng, Y J; Lam, C S
1994-01-01
String theories should reduce to ordinary four-dimensional field theories at low energies. Yet the formulation of the two are so different that such a connection, if it exists, is not immediately obvious. With the Schwinger proper-time representation, and the spinor helicity technique, it has been shown that field theories can indeed be written in a string-like manner, thus resulting in simplifications in practical calculations, and providing novel insights into gauge and gravitational theories. This paper continues the study of string organization of field theories by focusing on the question of local duality. It is shown that a single expression for the sum of many diagrams can indeed be written for QED, thereby simulating the duality property in strings. The relation between a single diagram and the dual sum is somewhat analogous to the relation between a old- fashioned perturbation diagram and a Feynman diagram. Dual expressions are particularly significant for gauge theories because they are gauge invari...
A gauge invariant theory for time dependent heat current
Chen, Jian; ShangGuan, Minhui; Wang, Jian
2015-05-01
In this work, we develop a general gauge-invariant theory for AC heat current through multi-probe systems. Using the non-equilibrium Green’s function, a general expression for time-dependent electrothermal admittance is obtained where we include the internal potential due to the Coulomb interaction explicitly. We show that the gauge-invariant condition is satisfied for heat current if the self-consistent Coulomb interaction is considered. It is known that the Onsager relation holds for dynamic charge conductance. We show in this work that the Onsager relation for electrothermal admittance is violated, except for a special case of a quantum dot system with a single energy level. We apply our theory to a nano capacitor where the Coulomb interaction plays an essential role. We find that, to the first order in frequency, the heat current is related to the electrochemical capacitance as well as the phase accumulated in the scattering event.
Manifestly Covariant Gauge-invariant Cosmological Perturbation Theory
Miedema, P G
2010-01-01
It is shown that a first-order cosmological perturbation theory for the open, flat and closed Friedmann-Lemaitre-Robertson-Walker universes admits one, and only one, gauge-invariant variable which describes the perturbation to the energy density and which becomes equal to the usual Newtonian energy density in the non-relativistic limit. The same holds true for the perturbation to the particle number density. Using these two new variables, a new manifestly gauge-invariant cosmological perturbation theory has been developed. Density perturbations evolve diabatically. Perturbations in the total energy density are gravitationally coupled to perturbations in the particle number density, irrespective of the nature of the particles. There is, in first-order, no back-reaction of perturbations to the global expansion of the universe. Small-scale perturbations in the radiation-dominated era oscillate with an increasing amplitude, whereas in older, less precise treatments, oscillating perturbations are found with a decr...
Institute of Scientific and Technical Information of China (English)
白永强; 刘震; 裴明
2008-01-01
The theory of moving frames developed by Peter J Olver and M Fels has importaut applications to geometry,classical invariant theory.We will use this theory to classify joint invariants and joint differential invariants of some transformation groups.
Robust topological degeneracy of classical theories
Vaezi, Mohammad-Sadegh; Ortiz, Gerardo; Nussinov, Zohar
2016-05-01
We challenge the hypothesis that the ground states of a physical system whose degeneracy depends on topology must necessarily realize topological quantum order and display nonlocal entanglement. To this end, we introduce and study a classical rendition of the Toric Code model embedded on Riemann surfaces of different genus numbers. We find that the minimal ground state degeneracy (and those of all levels) depends on the topology of the embedding surface alone. As the ground states of this classical system may be distinguished by local measurements, a characteristic of Landau orders, this example illustrates that topological degeneracy is not a sufficient condition for topological quantum order. This conclusion is generic and, as shown, it applies to many other models. We also demonstrate that certain lattice realizations of these models, and other theories, display a ground state entropy (and those of all levels) that is "holographic", i.e., extensive in the system boundary. We find that clock and U (1 ) gauge theories display topological (in addition to gauge) degeneracies.
Nilpotent Symmetries of a Diffeomorphism Invariant Theory: BRST Approach
Malik, R P
2016-01-01
Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism, we discuss the full set of proper BRST and anti-BRST transformations for a diffeomorphism invariant theory which is described by the Lagrangian density of a standard bosonic string (proposed by Kato and Ogawa). The above (anti-)BRST symmetry transformations are off-shell nilpotent and absolutely anticommuting. The latter property is valid on a constrained hypersurface in the two dimensional spacetime manifold (traced out by the propagation of the bosonic string) where the Curci-Ferrari (CF) type restriction is satisfied. This CF-type restriction is found to be an (anti-)BRST invariant quantity. We derive the precise form of the BRST and anti-BRST invariant Lagrangian densities as well as the exact expressions for the conserved (anti-)BRST and ghost charges of our present theory. The derivation of the proper anti-BRST symmetry transformations and the emergence of the CF-type restriction are completely novel results in our present investigation...
Effective Theory Approach to the Spontaneous Breakdown of Lorentz Invariance
Armendariz-Picon, Cristian; Penco, Riccardo
2010-01-01
We generalize the coset construction of Callan, Coleman, Wess and Zumino to theories in which the Lorentz group is spontaneously broken down to one of its subgroups. This allows us to write down the most general low-energy effective Lagrangian in which Lorentz invariance is non-linearly realized, and to explore the consequences of broken Lorentz symmetry without having to make any assumptions about the mechanism that triggers the breaking. We carry out the construction both in flat space, in which the Lorentz group is a global spacetime symmetry, and in a generally covariant theory, in which the Lorentz group can be treated as a local internal symmetry. As an illustration of this formalism, we construct the most general effective field theory in which the rotation group remains unbroken, and show that the latter is just the Einstein-aether theory.
Convolution of Lorentz Invariant Ultradistributions and Field Theory
Bollini, C G
2003-01-01
In this work, a general definition of convolution between two arbitrary four dimensional Lorentz invariant (fdLi) Tempered Ultradistributions is given, in both: Minkowskian and Euclidean Space (Spherically symmetric tempered ultradistributions). The product of two arbitrary fdLi distributions of exponential type is defined via the convolution of its corresponding Fourier Transforms. Several examples of convolution of two fdLi Tempered Ultradistributions are given. In particular we calculate exactly the convolution of two Feynman's massless propagators. An expression for the Fourier Transform of a Lorentz invariant Tempered Ultradistribution in terms of modified Bessel distributions is obtained in this work (Generalization of Bochner's formula to Minkowskian space). At the same time, and in a previous step used for the deduction of the convolution formula, we obtain the generalization to the Minkowskian space, of the dimensional regularization of the perturbation theory of Green Functions in the Euclidean conf...
Institute of Scientific and Technical Information of China (English)
ZHA Xin-Wei; MA Gang-Long
2011-01-01
It is a recent observation that entanglement classification for qubits is closely related to stochastic local operations and classical communication (SLOCC) invariants. Verstraete et al.[Phys. Rev. A 65 (2002)052112] showed that for pure states of four qubits there are nine different degenerate SLOCC entanglement classes. Li et al.[Phys.Rev. A 76 (2007)052311] showed that there are at least 28 distinct true SLOCC entanglement classes for four qubits by means of the SLOCC invariant and semi-invariant. We give 16 different entanglement classes for four qubits by means of basic SLOCC invariants.%@@ It is a recent observation that entanglement classification for qubits is closely related to stochastic local operations and classical communication (SLOCC) invariants.Verstraete et al.[Phys.Rev.A 65(2002)052112] showed that for pure states of four qubits there are nine different degenerate SLOCC entanglement classes.Li et al.[Phys.Rev.A 76(2007)052311] showed that there are at least 28 distinct true SLOCC entanglement classes for four qubits by means of the SLOCC invariant and semi-invariant.We give 16 different entanglement classes for four qubits by means of basic SLOCC invariants.
Extending classical molecular theory with polarization.
Keyes, Tom; Napoleon, Raeanne L
2011-01-27
A classical, polarizable, electrostatic theory of short-ranged atom-atom interactions, incorporating the smeared nature of atomic partial charges, is presented. Detailed models are constructed for CO monomer and for CO interacting with an iron atom, as a first step toward heme proteins. A good representation is obtained of the bond-length-dependent dipole of CO monomer from fitting at the equilibrium distance only. Essential features of the binding of CO to myoglobin (Mb) and model heme compounds, including the binding energy, the position of the minimum in the Fe-C potential, the Fe-C frequency, the bending energy, the linear geometry of FeCO, and the increase of the Stark tuning rate and IR intensity, are obtained, suggesting that a substantial part of the Fe-CO interaction consists of a classical, noncovalent, "electrostatic bond ". The binding energy is primarily polarization energy, and the polarization energy of an OH pair in water is shown to be comparable to the experimental hydrogen bond energy.
Noncommutative field theory and violation of translation invariance
Energy Technology Data Exchange (ETDEWEB)
Bertolami, Orfeu [Departamento de Fisica, Instituto Superior Tecnico, Lisbon (Portugal)]. E-mail: orfeu@cosmos.ist.utl.pt; Guisado, Luis [Departamento de Fisica, Instituto Superior Tecnico, Lisbon (Portugal)
2003-12-01
Noncommutative field theories with commutator of the coordinates of the form [x{sup {mu}}, x{sup {nu}}] = i {lambda}{sup {mu}}{sup {nu}}{sub {omega}}x{sup {omega}} with nilpotent structure constants are studied and shown that a free quantum field theory is not affected. Invariance under translations is broken and the conservation of energy-momentum is violated, obeying a new law which is expressed by a Poincare-invariant equation. The resulting new kinematics is studied and applied to simple examples and to astrophysical puzzles, such as the observed violation of the GZK cutoff. The {lambda}{phi}{sup 4} quantum field theory is also considered in this context. In particular, self interaction terms violate the usual conservation of energy-momentum and, hence, the radiative correction to the propagator is altered. The correction to first order in {lambda} is calculated. The usual UV divergent terms are still present, but a new type of term also emerges, which is IR divergent, violates momentum conservation and implies a correction to the dispersion relation. (author)
Unified Field Theory and Principle of Representation Invariance
Ma, Tian
2012-01-01
This is part of a research program to establish a unified field model for interactions in nature. The aim of this article is to postulate a new principle of representation invariance (PRI), to provide a needed mathematical foundation for PRI, and to use PRI to refine the unified field equations of four interactions. Intuitively, PRI amounts to saying that all SU(N) gauge theories should be invariant under transformations of different representations of SU(N). With PRI, we are able to substantially reduce the number of to-be-determined parameters in the unified model to two SU(2) and SU(3) constant vectors $\\{\\alpha^1_\\mu \\}$ and $\\{\\alpha^2_k\\}$, containing 11 parameters, which represent the portions distributed to the gauge potentials by the weak and strong charges. Furthermore, both PRI and PID can be directly applied to individual interactions, leading to a unified theory for dark matter and dark energy, and theories on strong and weak interaction potentials. As a direct application of the strong interacti...
Invariant slow-roll parameters in scalar-tensor theories
Kuusk, Piret; Rünkla, Mihkel; Saal, Margus; Vilson, Ott
2016-10-01
A general scalar-tensor theory can be formulated in different parametrizations that are related by a conformal rescaling of the metric and a scalar field redefinition. We compare formulations of slow-roll regimes in the Einstein and Jordan frames using quantities that are invariant under the conformal rescaling of the metric and transform as scalar functions under the reparametrization of the scalar field. By comparing spectral indices, calculated up to second order, we find that the frames are equivalent up to this order, due to the underlying assumptions.
Shear viscosity of the $\\Phi^4$ theory from classical simulation
Homor, M M
2015-01-01
Shear viscosity of the classical $\\Phi^4$ theory is measured using classical microcanonical simulation. To calculate the Kubo formula, we measure the energy-momentum tensor correlation function, and apply the Green-Kubo relation. Being a classical theory, the results depend on the cutoff which should be chosen in the range of the temperature. Comparison with experimentally accessible systems is also performed.
On Conservation Forms and Invariant Solutions for Classical Mechanics Problems of Liénard Type
Directory of Open Access Journals (Sweden)
Gülden Gün Polat
2014-01-01
Full Text Available In this study we apply partial Noether and λ-symmetry approaches to a second-order nonlinear autonomous equation of the form y′′+fyy′+g(y=0, called Liénard equation corresponding to some important problems in classical mechanics field with respect to f(y and g(y functions. As a first approach we utilize partial Lagrangians and partial Noether operators to obtain conserved forms of Liénard equation. Then, as a second approach, based on the λ-symmetry method, we analyze λ-symmetries for the case that λ-function is in the form of λ(x,y,y′=λ1(x,yy′+λ2(x,y. Finally, a classification problem for the conservation forms and invariant solutions are considered.
Dark Matter from a Classically Scale-Invariant $SU(3)_X$
Karam, Alexandros
2016-01-01
In this work we study a classically scale-invariant extension of the Standard Model in which the dark matter and electroweak scales are generated through the Coleman-Weinberg mechanism. The extra $SU(3)_X$ gauge factor gets completely broken by the vevs of two scalar triplets. Out of the eight resulting massive vector bosons the three lightest are stable due to an intrinsic $Z_2\\times Z_2'$ discrete symmetry and can constitute dark matter candidates. We analyze the phenomenological viability of the predicted multi-Higgs sector imposing theoretical and experimental constraints. We perform a comprehensive analysis of the dark matter predictions of the model solving numerically the set of coupled Boltzmann equations involving all relevant dark matter processes and explore the direct detection prospects of the dark matter candidates.
Dark matter and neutrino masses from a classically scale-invariant multi-Higgs portal
Karam, Alexandros
2016-01-01
We present a classically scale-invariant model where the dark matter, neutrino and electroweak mass scales are dynamically generated from dimensionless couplings. The Standard Model gauge sector is extended by a dark $SU(2)_X$ gauge symmetry that is completely broken through a complex scalar doublet via the Coleman-Weinberg mechanism. The three resulting dark vector bosons of equal mass are stable and can play the role of dark matter. We also incorporate right-handed neutrinos which are coupled to a real singlet scalar that communicates with the other scalars through portal interactions. The multi-Higgs sector is analyzed by imposing theoretical and experimental constraints. We compute the dark matter relic abundance and study the possibility of the direct detection of the dark matter candidate from XENON 1T.
Dark matter from a classically scale-invariant S U (3 )X
Karam, Alexandros; Tamvakis, Kyriakos
2016-09-01
In this work we study a classically scale-invariant extension of the Standard Model in which the dark matter and electroweak scales are generated through the Coleman-Weinberg mechanism. The extra S U (3 )X gauge factor gets completely broken by the vacuum expectation values of two scalar triplets. Out of the eight resulting massive vector bosons the three lightest are stable due to an intrinsic Z2×Z2' discrete symmetry and can constitute dark matter candidates. We analyze the phenomenological viability of the predicted multi-Higgs sector imposing theoretical and experimental constraints. We perform a comprehensive analysis of the dark matter predictions of the model solving numerically the set of coupled Boltzmann equations involving all relevant dark matter processes and explore the direct detection prospects of the dark matter candidates.
Fisher information and quantum-classical field theory: classical statistics similarity
Energy Technology Data Exchange (ETDEWEB)
Syska, J. [Department of Field Theory and Particle Physics, Institute of Physics, University of Silesia, Uniwersytecka 4, 40-007 Katowice (Poland)
2007-07-15
The classical statistics indication for the impossibility to derive quantum mechanics from classical mechanics is proved. The formalism of the statistical Fisher information is used. Next the Fisher information as a tool of the construction of a self-consistent field theory, which joins the quantum theory and classical field theory, is proposed. (copyright 2007 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
The energy–momentum tensor(s in classical gauge theories
Directory of Open Access Journals (Sweden)
Daniel N. Blaschke
2016-11-01
Full Text Available We give an introduction to, and review of, the energy–momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space–time. For the canonical energy–momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy–momentum tensor. The relationship with the Einstein–Hilbert tensor following from the coupling to a gravitational field is also discussed.
The Energy-Momentum Tensor(s) in Classical Gauge Theories
Blaschke, Daniel N; Reboud, Meril; Schweda, Manfred
2016-01-01
We give an introduction to, and review of, the energy-momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space-time. For the canonical energy-momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy-momentum tensor. The relationship with the Einstein-Hilbert tensor following from the coupling to a gravitational field is also discussed.
Schroedinger Invariance from Lifshitz Isometries in Holography and Field Theory
Hartong, Jelle; Obers, Niels A
2014-01-01
We study non-relativistic field theory coupled to a torsional Newton-Cartan geometry both directly as well as holographically. The latter involves gravity on asymptotically locally Lifshitz space-times. We define an energy-momentum tensor and a mass current and study the relation between conserved currents and conformal Killing vectors for flat Newton-Cartan backgrounds. It is shown that this involves two different copies of the Lifshitz algebra together with an equivalence relation that joins these two Lifshitz algebras into a larger Schroedinger algebra (without the central element). In the holographic setup this reveals a novel phenomenon in which a large bulk diffeomorphism is dual to a discrete gauge invariance of the boundary field theory.
Hilbert space theory of classical electrodynamics
Indian Academy of Sciences (India)
RAJAGOPAL A K; GHOSE PARTHA
2016-06-01
Classical electrodynamics is reformulated in terms of wave functions in the classical phase space of electrodynamics, following the Koopman–von Neumann–Sudarshan prescription for classical mechanics on Hilbert spaces sans the superselection rule which prohibits interference effects in classical mechanics. This is accomplished by transforming from a set of commutingobservables in one Hilbert space to another set of commuting observables in a larger Hilbert space. This is necessary to clarify the theoretical basis of the much recent work on quantum-like features exhibited by classical optics. Furthermore, following Bondar et al, {\\it Phys. Rev.} A 88, 052108 (2013), it is pointed out that quantum processes that preserve the positivity or nonpositivity of theWigner function can be implemented by classical optics. This may be useful in interpreting quantum information processing in terms of classical optics.
Gauge invariance and radiative corrections in an extra dimensional theory
Novales-Sánchez, H.; Toscano, J. J.
2011-04-01
The gauge structure of the four dimensional effective theory originated in a pure five dimensional Yang-Mills theory compactified on the orbifold S1 /Z2, is discussed on the basis of the BRST symmetry. If gauge parameters propagate in the bulk, the excited Kaluza-Klein (KK) modes are gauge fields and the four dimensional theory is gauge invariant only if the compactification is carried out by using curvatures as fundamental objects. The four dimensional theory is governed by two types of gauge transformations, one determined by the KK zero modes of the gauge parameters and the other by the excited ones. Within this context, a gauge-fixing procedure to quantize the KK modes that is covariant under the first type of gauge transformations is shown and the ghost sector induced by the gauge-fixing functions is presented. If the gauge parameters are confined to the usual four dimensional space-time, the known result in the literature is reproduced with some minor variants, although it is emphasized that the excited KK modes are not gauge fields, but matter fields transforming under the adjoint representation of SU4(N). A calculation of the one-loop contributions of the excited KK modes of the SUL(2) gauge group on the off-shell W+W-V, with V a photon or a Z boson, is exhibited. Such contributions are free of ultraviolet divergences and well-behaved at high energies.
Holographic Fluctuations from Unitary de Sitter Invariant Field Theory
Banks, Tom; Torres, T J; Wainwright, Carroll L
2013-01-01
We continue the study of inflationary fluctuations in Holographic Space Time models of inflation. We argue that the holographic theory of inflation provides a physical context for what is often called dS/CFT. The holographic theory is a quantum theory which, in the limit of a large number of e-foldings, gives rise to a field theory on $S^3$, which is the representation space for a unitary representation of SO(1,4). This is not a conventional CFT, and we do not know the detailed non-perturbative axioms for correlation functions. However, the two- and three-point functions are completely determined by symmetry, and coincide up to a few constants (really functions of the background FRW geometry) with those calculated in a single field slow-roll inflation model. The only significant deviation from slow roll is in the tensor fluctuations. We predict zero tensor tilt and roughly equal weight for all three conformally invariant tensor 3-point functions (unless parity is imposed as a symmetry). We discuss the relatio...
Classical and semi-classical solutions of the Yang--Mills theory. [Review
Energy Technology Data Exchange (ETDEWEB)
Jackiw, R.; Nohl, C.; Rebbi, C.
1977-12-01
This review summarizes what is known at present about classical solutions to Yang-Mills theory both in Euclidean and Minkowski space. The quantal meaning of these solutions is also discussed. Solutions in Euclidean space expose multiple vacua and tunnelling of the quantum theory. Those in Minkowski space-time provide a semi-classical spectrum for a conformal generator.
A gauge-invariant reorganization of thermal gauge theory
Energy Technology Data Exchange (ETDEWEB)
Su, Nan
2010-07-01
This dissertation is devoted to the study of thermodynamics for quantum gauge theories. The poor convergence of quantum field theory at finite temperature has been the main obstacle in the practical applications of thermal QCD for decades. In this dissertation I apply hard-thermal-loop perturbation theory, which is a gauge-invariant reorganization of the conventional perturbative expansion for quantum gauge theories to the thermodynamics of QED and Yang-Mills theory to three-loop order. For the Abelian case, I present a calculation of the free energy of a hot gas of electrons and photons by expanding in a power series in m{sub D}/T, m{sub f}/T and e{sup 2}, where m{sub D} and m{sub f} are the photon and electron thermal masses, respectively, and e is the coupling constant. I demonstrate that the hard-thermal-loop perturbation reorganization improves the convergence of the successive approximations to the QED free energy at large coupling, e {proportional_to} 2. For the non-Abelian case, I present a calculation of the free energy of a hot gas of gluons by expanding in a power series in m{sub D}/T and g{sup 2}, where m{sub D} is the gluon thermal mass and g is the coupling constant. I show that at three-loop order hard-thermal-loop perturbation theory is compatible with lattice results for the pressure, energy density, and entropy down to temperatures T {proportional_to} 2 - 3 T{sub c}. The results suggest that HTLpt provides a systematic framework that can be used to calculate static and dynamic quantities for temperatures relevant at LHC. (orig.)
Covariant and locally Lorentz-invariant varying speed of light theories
Magueijo, J
2000-01-01
We propose definitions for covariance and local Lorentz invariance applicable when the speed of light $c$ is allowed to vary. They have the merit of retaining only those aspects of the usual definitions which are invariant under unit transformations, and which can therefore legitimately represent the outcome of an experiment. We then discuss some possibilities for invariant actions governing the dynamics of such theories. We consider first the classical action for matter fields and the effects of a changing $c$ upon quantization. We discover a peculiar form of quantum particle creation due to a varying $c$. We then study actions governing the dynamics of gravitation and the speed of light. We find the free, empty-space, no-gravity solution, to be interpreted as the counterpart of Minkowksi space-time, and highlight its similarities with Fock-Lorentz space-time. We also find flat-space string-type solutions, in which near the string core $c$ is much higher. We label them fast-tracks and compare them with gravi...
Bassetto, A; Torrielli, A; Vian, F
2005-01-01
We present an investigation on the invariance properties of noncommutative Yang-Mills theory in two dimensions under area preserving diffeomorphisms. Stimulated by recent remarks by Ambjorn, Dubin and Makeenko who found a breaking of such an invariance, we confirm both on a fairly general ground and by means of perturbative analytical and numerical calculations that indeed invariance under area preserving diffeomorphisms is lost. However a remnant survives, namely invariance under linear unimodular tranformations.
Introducing quantum effects in classical theories
Fabris, J C; Rodrigues, D C; Daouda, M H
2015-01-01
In this paper, we explore two different ways of implementing quantum effects in a classical structure. The first one is through an external field. The other one is modifying the classical conservation laws. In both cases, the consequences for the description of the evolution of the universe are discussed.
Palmer, T N
2012-01-01
A realistic measurement-free theory for the quantum physics of multiple qubits is proposed. This theory is based on a symbolic representation of a fractal state-space geometry which is invariant under the action of deterministic and locally causal dynamics. This symbolic representation is constructed from self-similar families of quaternionic operators. Using number-theoretic properties of the cosine function, the statistical properties of the symbolic representation of the invariant set are shown to be consistent with the contextual requirements of the Kochen-Specker theorem, are not constrained by Bell inequalities, and mirror the statistics of entangled qubits. These number-theoretic properties in turn reflect the sparseness of the invariant set in state space, and relate to the metaphysical notion of counterfactual incompleteness. Using the concept of probability, the complex Hilbert Space can be considered the completion of this symbolic representation into the state space continuum. As a result, it is p...
Functional methods underlying classical mechanics, relativity and quantum theory
Kryukov, Alexey A.
2013-01-01
The paper investigates the physical content of a recently proposed mathematical framework that unifies the standard formalisms of classical mechanics, relativity and quantum theory. In the framework states of a classical particle are identified with Dirac delta functions. The classical space is "made" of these functions and becomes a submanifold in a Hilbert space of states of the particle. The resulting embedding of the classical space into the space of states is highly non-trivial and accou...
Introduction to Classical Density Functional Theory by a Computational Experiment
Jeanmairet, Guillaume; Levy, Nicolas; Levesque, Maximilien; Borgis, Daniel
2014-01-01
We propose an in silico experiment to introduce the classical density functional theory (cDFT). Density functional theories, whether quantum or classical, rely on abstract concepts that are nonintuitive; however, they are at the heart of powerful tools and active fields of research in both physics and chemistry. They led to the 1998 Nobel Prize in…
Reconstruction of the standard model with classical conformal invariance in noncommutative geometry
Yang, Masaki J S
2015-01-01
In this paper, we derive the standard model with classical conformal invariance from the Yang--Mills--Higgs model in noncommutative geometry (NCG). In the ordinary context of the NCG, the {\\it distance matrix} $M_{nm}$ which corresponds to the vacuum expectation value of Higgs fields is taken to be finite. However, since $M_{nm}$ is arbitrary in this formulation, we can take all $M_{nm}$ to be zero. In the original composite scheme, the Higgs field itself vanishes with the condition $M_{nm} = 0$. Then, we adopt the elemental scheme, in which the gauge and the Higgs bosons are regarded as elemental fields. By these assumptions, all scalars do not have vevs at tree level. The symmetry breaking mechanism will be implemented by the Coleman--Weinberg mechanism. As a result, we show a possibility to solve the hierarchy problem in the context of NCG. Unfortunately, the Coleman--Weinberg mechanism does not work in the SM Higgs sector, because the Coleman--Weinberg effective potential becomes unbounded from below for ...
Múnera, Héctor A.
2016-07-01
It is postulated that there exists a fundamental energy-like fluid, which occupies the flat three-dimensional Euclidean space that contains our universe, and obeys the two basic laws of classical physics: conservation of linear momentum, and conservation of total energy; the fluid is described by the classical wave equation (CWE), which was Schrödinger's first candidate to develop his quantum theory. Novel solutions for the CWE discovered twenty years ago are nonharmonic, inherently quantized, and universal in the sense of scale invariance, thus leading to quantization at all scales of the universe, from galactic clusters to the sub-quark world, and yielding a unified Lorentz-invariant quantum theory ab initio. Quingal solutions are isomorphic under both neo-Galilean and Lorentz transformations, and exhibit nother remarkable property: intrinsic unstability for large values of ℓ (a quantum number), thus limiting the size of each system at a given scale. Unstability and scale-invariance together lead to nested structures observed in our solar system; unstability may explain the small number of rows in the chemical periodic table, and nuclear unstability of nuclides beyond lead and bismuth. Quingal functions lend mathematical basis for Boscovich's unified force (which is compatible with many pieces of evidence collected over the past century), and also yield a simple geometrical solution for the classical three-body problem, which is a useful model for electronic orbits in simple diatomic molecules. A testable prediction for the helicoidal-type force is suggested.
Knot invariants and higher representation theory II: the categorification of quantum knot invariants
Webster, Ben
2010-01-01
We construct knot invariants categorifying the quantum knot variants for all representations of quantum groups. We show that these invariants coincide with previous invariants defined by Khovanov for sl_2 and sl_3 and by Mazorchuk-Stroppel and Sussan for sl_n. We also suggest an approach to showing that these knot homologies are functorial. Our technique uses categorifications of the tensor products of integrable representations of Kac-Moody algebras and quantum groups, constructed a prequel to this paper. In particular, we construct functors on these categorifying the action of the braiding and duality of quantum group representations. These categories are based on the pictorial approach of Khovanov and Lauda.
Buitrago, J.
A new classical 2-spinor approach to U(1) gauge theory is presented in which the usual four-potential vector field is replaced by a symmetric second rank spinor. Following a lagrangian formulation, it is shown that the four-rank spinor representing the Maxwell field tensor has a U(1) local gauge invariance in terms of the electric and magnetic field strengths. When applied to the magnetic field of a monopole, this formulation, via the irreducible representation condition for the gauge group, leads to a quantization condition differing by a factor 2 of the one predicted by Dirac without relying on any kind of singular vector potentials. Finally, the U(1) invariant spinor equations, are applied to electron magnetic resonance which has many applications in the study of materials.
On the classical theory of molecular optical activity
Frolov, Alexei M
2010-01-01
The basic principles of classical and semi-classical theories of molecular optical activity are discussed. These theories are valid for dilute solutions of optically active organic molecules. It is shown that all phenomena known in the classical theory of molecular optical activity can be described with the use of one pseudo-scalar which is a uniform function of the incident light frequency $\\omega$. The relation between optical rotation and circular dichroism is derived from the basic Kramers-Kronig relations. In our discussion of the general theory of molecular optical activity we introduce the tensor of molecular optical activity. It is shown that to evaluate the optical rotation and circular dichroism at arbitrary frequencies one needs to know only nine (3 + 6) molecular tensors. The quantum (or semi-classical) theory of molecular optical activity is also briefly discussed. We also raise the possibility of measuring the optical rotation and circular dichroism at wavelengths which correspond to the vacuum ...
HCI Theory Classical, Modern, and Contemporary
Rogers, Yvonne
2012-01-01
Theory is the bedrock of many sciences, providing a rigorous method toadvance knowledge through testing and falsifying hypotheses aboutobservable phenomena. To begin with, the nascent field of HCI followedsuit, borrowing theories from cognitive science to test theories aboutuser performance at the interface.But HCI has emerged as an eclectic interdiscipline rather than a welldefinedscience. It now covers all aspects of human life, from birth tobereavement, through all manner of computing, from device ecologiesto nanotechnology. It comes as no surprise that the role of theory in HCIhas also gre
The Kubelka-Munk Theory for Color Image Invariant Properties
Geusebroek, J.M.; Gevers, Th.; Smeulders, A.W.M.
2002-01-01
A fundamental problem in color image processing is the integration of the physical laws of light reflection into image processing results, the probem known as photometric invariance. The derivation of object properties from color images yields the extraction of geometric and photometric invariants f
Classical Solutions of SU(3) Pure Yang-Mills Theory
2002-01-01
Regular classical solutions of pure SU(3) gauge theories, in Minkowsky spacetime, are computed in the Landau gauge. The classical fields have an intrinsic energy scale and produce quark confinement if interpreted in the sense of a nonrelativistic potential. Moreover, the quark propagator in the background of these fields vanishes at large positive and negative time and space separations.
Variational principles for multisymplectic second-order classical field theories
Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso
2015-06-01
We state a unified geometrical version of the variational principles for second-order classical field theories. The standard Lagrangian and Hamiltonian variational principles and the corresponding field equations are recovered from this unified framework.
Variational principles for multisymplectic second-order classical field theories
Román Roy, Narciso; Prieto Martínez, Pedro Daniel
2015-01-01
We state a unified geometrical version of the variational principles for second-order classical field theories. The standard Lagrangian and Hamiltonian variational principles and the corresponding field equations are recovered from this unified framework. Peer Reviewed
Classical conformality in the Standard Model from Coleman's theory
Kawana, Kiyoharu
2016-01-01
The classical conformality is one of the possible candidates for explaining the gauge hierarchy of the Standard Model. We show that it is naturally obtained from the Coleman's theory on baby universe.
Experimental assessment of unvalidated assumptions in classical plasticity theory.
Energy Technology Data Exchange (ETDEWEB)
Brannon, Rebecca Moss (University of Utah, Salt Lake City, UT); Burghardt, Jeffrey A. (University of Utah, Salt Lake City, UT); Bauer, Stephen J.; Bronowski, David R.
2009-01-01
This report investigates the validity of several key assumptions in classical plasticity theory regarding material response to changes in the loading direction. Three metals, two rock types, and one ceramic were subjected to non-standard loading directions, and the resulting strain response increments were displayed in Gudehus diagrams to illustrate the approximation error of classical plasticity theories. A rigorous mathematical framework for fitting classical theories to the data, thus quantifying the error, is provided. Further data analysis techniques are presented that allow testing for the effect of changes in loading direction without having to use a new sample and for inferring the yield normal and flow directions without having to measure the yield surface. Though the data are inconclusive, there is indication that classical, incrementally linear, plasticity theory may be inadequate over a certain range of loading directions. This range of loading directions also coincides with loading directions that are known to produce a physically inadmissible instability for any nonassociative plasticity model.
Quantitative methods in classical perturbation theory.
Giorgilli, A.
Poincaré proved that the series commonly used in Celestial mechanics are typically non convergent, although their usefulness is generally evident. Recent work in perturbation theory has enlightened this conjecture of Poincaré, bringing into evidence that the series of perturbation theory, although non convergent in general, furnish nevertheless valuable approximations to the true orbits for a very large time, which in some practical cases could be comparable with the age of the universe. The aim of the author's paper is to introduce the quantitative methods of perturbation theory which allow to obtain such powerful results.
CLASSICAL ELECTRON THEORY FROM A MODERN STANDPOINT
occurrence and removal of runaway modes, the radiation from a uniformly accelerated charge, an the relation between Maxwell’s electrodynamics and the action-at-a-distance theory of Wheeler and Feynman . (Author)
On p -form theories with gauge invariant second order field equations
Deffayet, Cédric; Mukohyama, Shinji; Sivanesan, Vishagan
2016-04-01
We explore field theories of a single p -form with equations of motions of order strictly equal to 2 and gauge invariance. We give a general method for the classification of such theories which are extensions to the p -forms of the Galileon models for scalars. Our classification scheme allows us to compute an upper bound on the number of different such theories depending on p and on the space-time dimension. We are also able to build a nontrivial Galileon-like theory for a 3-form with gauge invariance and an action which is polynomial into the derivatives of the form. This theory has gauge invariant field equations but an action which is not, like a Chern-Simons theory. Hence the recently discovered no-go theorem stating that there are no nontrivial gauge invariant vector Galileons (which we are also able here to confirm with our method) does not extend to other odd-p cases.
On p-form theories with gauge invariant second order field equations
Deffayet, Cédric; Sivanesan, Vishagan
2016-01-01
We explore field theories of a single p-form with equations of motions of order strictly equal to two and gauge invariance. We give a general method for the classification of such theories which are extensions to the p-forms of the Galileon models for scalars. Our classification scheme allows to compute an upper bound on the number of different such theories depending on p and on the space-time dimension. We are also able to build a non trivial Galileon like theory for a 3-form with gauge invariance and an action which is polynomial into the derivatives of the form. This theory has gauge invariant field equations but an action which is not, like a Chern-Simons theory. Hence the recently discovered no-go theorem stating that there are no non trivial gauge invariant vector Galileons (which we are also able here to confirm with our method) does not extend to other odd p cases.
On invariants and scalar chiral correlation functions in N=1 superconformal field theories
Knuth, Holger
2010-01-01
A general expression for the four-point function with vanishing total R-charge of anti-chiral and chiral superfields in N=1 superconformal theories is given. It is obtained by applying the exponential of a simple universal nilpotent differential operator to an arbitrary function of two cross ratios. To achieve this the nilpotent superconformal invariants according to Park are focused. Several dependencies between these invariants are presented, so that eight nilpotent invariants and 27 monomi...
Strongly first-order electroweak phase transition and classical scale invariance
Farzinnia, Arsham; Ren, Jing
2014-10-01
In this work, we examine the possibility of realizing a strongly first-order electroweak phase transition within the minimal classically scale-invariant extension of the standard model (SM), previously proposed and analyzed as a potential solution to the hierarchy problem. By introducing one complex gauge-singlet scalar and three (weak scale) right-handed Majorana neutrinos, the scenario was successfully rendered capable of achieving a radiative breaking of the electroweak symmetry (by means of the Coleman-Weinberg mechanism), inducing nonzero masses for the SM neutrinos (via the seesaw mechanism), presenting a pseudoscalar dark matter candidate (protected by the CP symmetry of the potential), and predicting the existence of a second CP-even boson (with suppressed couplings to the SM content) in addition to the 125 GeV scalar. In the present treatment, we construct the full finite-temperature one-loop effective potential of the model, including the resummed thermal daisy loops, and demonstrate that finite-temperature effects induce a first-order electroweak phase transition. Requiring the thermally driven first-order phase transition to be sufficiently strong at the onset of the bubble nucleation (corresponding to nucleation temperatures TN˜100-200 GeV) further constrains the model's parameter space; in particular, an O(0.01) fraction of the dark matter in the Universe may be simultaneously accommodated with a strongly first-order electroweak phase transition. Moreover, such a phase transition disfavors right-handed Majorana neutrino masses above several hundreds of GeV, confines the pseudoscalar dark matter masses to ˜1-2 TeV, predicts the mass of the second CP-even scalar to be ˜100-300 GeV, and requires the mixing angle between the CP-even components of the SM doublet and the complex singlet to lie within the range 0.2≲sinω ≲0.4. The obtained results are displayed in comprehensive exclusion plots, identifying the viable regions of the parameter space
Functional methods underlying classical mechanics, relativity and quantum theory
Kryukov, A.
2013-04-01
The paper investigates the physical content of a recently proposed mathematical framework that unifies the standard formalisms of classical mechanics, relativity and quantum theory. In the framework states of a classical particle are identified with Dirac delta functions. The classical space is "made" of these functions and becomes a submanifold in a Hilbert space of states of the particle. The resulting embedding of the classical space into the space of states is highly non-trivial and accounts for numerous deep relations between classical and quantum physics and relativity. One of the most striking results is the proof that the normal probability distribution of position of a macroscopic particle (equivalently, position of the corresponding delta state within the classical space submanifold) yields the Born rule for transitions between arbitrary quantum states.
Classical Coupled Mode Theory of Optomechanical Crystals
Khorasani, Sina
2016-01-01
Acousto-optic interaction in optomechanical crystals allows unidirectional control of elastic waves over optical waves. However, as a result of this nonlinear interaction, infinitely many optical modes are born. This article presents an exact formulaion of coupled mode theory for interaction between elastic Bloch wave waves and photonic Bloch waves moving in a phonotonic waveguide. In general, an optical wavefront is strongly diffracted by an elastic wave in frequency and wavevector, and thus infinite modes with different frequencies and wavevectors appear. We discuss resonance and mode conversion conditions, and present a rigorous method to derive coupling rates and mode profiles. We also find a conservation law which rules over total optical power from interacting individual modes. Modifications of the theory to phonotonic cavities are also discussed. We present application examples including switch, frequency shifter, and reflector.
On invariants and scalar chiral correlation functions in N=1 superconformal field theories
Knuth, Holger
2010-01-01
A general expression for the four-point function with vanishing total R-charge of anti-chiral and chiral superfields in N=1 superconformal theories is given. It is obtained by applying the exponential of a simple universal nilpotent differential operator to an arbitrary function of two cross ratios. To achieve this the nilpotent superconformal invariants according to Park are focused. Several dependencies between these invariants are presented, so that eight nilpotent invariants and 27 monomials of these invariants of degree d>2 are left being linearly independent. It is analyzed, how terms within the four-point function of general scalar superfields cancel in order to fulfill the chiral restrictions.
On Invariants and Scalar Chiral Correlation Functions in { n} = 1 Superconformal Field Theories
Knuth, Holger
A general expression for the four-point function with vanishing total R-charge of antichiral and chiral superfields in { N} = 1 superconformal theories is given. It is obtained by applying the exponential of a simple universal nilpotent differential operator to an arbitrary function of two cross-ratios. To achieve this the nilpotent superconformal invariants according to Park are focused. Several dependencies between these invariants are presented, so that eight nilpotent invariants and 27 monomials of these invariants of degree d > 1 are left being linearly independent. It is analyzed, how terms within the four-point function of general scalar superfields cancel in order to fulfill the chiral restrictions.
Satin, Seema
2015-01-01
We attempt to introduce an new approach towards study of certain interesting issues in classical gravity. This can be done for few confined, but interesting and meaningful physical situations, which can be modeled by a classical stochastic Einstein equation. The Einstein equation can be looked upon as an equation of motion, while introducing to it a classical stochastic source or classical fluctuations as driving source. This is analogous to the Langevin equation formalism, in Brownian motion studies. A justification for the validity of such an ansatz for classical gravity is given. The regime of validity of such an approach and the consequences and possible outcomes of this formulation are discussed. We also mention, further relevant directions and applications of the same,that act as motivation towards the new proposal. This field of study can be seen to emerge out of well established ideas and results in Brownian motion theory as well as the Stochastic Semiclassical Gravity (which is already an active area...
Scale Invariant Kaluza-Klein Theory and the Fate of the Gravitational Collapse
Quirós, I
2002-01-01
Pushing forward the similitudes between the gravitational collapse and the expansion of the universe (in the reversed sense of time), it should be expected that, during the collapse, eventually, a spacetime domain would be reached where attained energy scales are very high. In consequence some of the compactified extra dimensions may be decompactified and some presently broken symmetries may be restored. A more fundamental theory (of which Einstein's theory is a symmetry broken phase) is then expected to take account of further description of the collapse. I propose a simple (classical) model for the description of the late stages of the gravitational collapse: A non-Riemannian, scale-invariant version of 5-dimensional Kaluza-Klein theory in which the standard Riemann structure of the higher-dimensional manifold is replaced by a Weyl-integrable one. A class of solutions, that generalize the "soliton" one by Gross and Perry and Davidson and Owen, is found. This class contains both naked singularities and wormh...
Homotopy Theory of Probability Spaces I: Classical independence and homotopy Lie algebras
Park, Jae-Suk
2015-01-01
This is the first installment of a series of papers whose aim is to lay a foundation for homotopy probability theory by establishing its basic principles and practices. The notion of a homotopy probability space is an enrichment of the notion of an algebraic probability space with ideas from algebraic homotopy theory. This enrichment uses a characterization of the laws of random variables in a probability space in terms of symmetries of the expectation. The laws of random variables are reinterpreted as invariants of the homotopy types of infinity morphisms between certain homotopy algebras. The relevant category of homotopy algebras is determined by the appropriate notion of independence for the underlying probability theory. This theory will be both a natural generalization and an effective computational tool for the study of classical algebraic probability spaces, while keeping the same central limit. This article is focused on the commutative case, where the laws of random variables are also described in t...
Lectures on classical and quantum theory of fields
Energy Technology Data Exchange (ETDEWEB)
Arodz, Henryk; Hadasz, Leszek [Jagiellonian Univ., Krakow (Poland). Inst. Physics
2010-07-01
This textbook on classical and quantum theory of fields addresses graduate students starting to specialize in theoretical physics. It provides didactic introductions to the main topics in the theory of fields, while taking into account the contemporary view of the subject. The student will find concise explanations of basic notions essential for applications of the theory of fields as well as for frontier research in theoretical physics. One third of the book is devoted to classical fields. Each chapter contains exercises of varying degree of difficulty with hints or solutions, plus summaries and worked examples as useful. The textbook is based on lectures delivered to students of theoretical physics at Jagiellonian University. It aims to deliver a unique combination of classical and quantum field theory in one compact course. (orig.)
Lectures on Classical and Quantum Theory of Fields
Arodź, Henryk
2010-01-01
This textbook on classical and quantum theory of fields addresses graduate students starting to specialize in theoretical physics. It provides didactic introductions to the main topics in the theory of fields, while taking into account the contemporary view of the subject. The student will find concise explanations of basic notions essential for applications of the theory of fields as well as for frontier research in theoretical physics. One third of the book is devoted to classical fields. Each chapter contains exercises of varying degree of difficulty with hints or solutions, plus summaries and worked examples as useful. The textbook is based on lectures delivered to students of theoretical physics at Jagiellonian University. It aims to deliver a unique combination of classical and quantum field theory in one compact course.
Introduction to Classical Density Functional Theory by Computational Experiment
Jeanmairet, Guillaume; Levesque, Maximilien; Borgis, Daniel
2014-01-01
We present here an introductory practical course to classical density functional theory (cDFT). Density functional theories, whether quantum or classical, rely largely on nonintuitive abstract concepts and applied mathematics. They are nevertheless a powerful tool and an active field of research in physics and chemistry that led to the 1998 Nobel prize in chemistry. We here illustrate the DFT in its most mathematically simple and yet physically relevant form: the classical density functional theory of an ideal fluid in an external field, as applied to the prediction of the structure of liquid neon at the molecular scale. This introductory course is built around the production of a cDFT code written by students using the Mathematica language. In this way, they are brought to deal with (i) the cDFT theory itself, (ii) some basic concepts around the statistical mechanics of simple fluids, (iii) the underlying mathematical and numerical problem of functional minimization, and (iv) a functional programming languag...
Gauge bridges in classical field theory; Eichbruecken in der klassischen Feldtheorie
Energy Technology Data Exchange (ETDEWEB)
Jakobs, S.
2009-03-15
In this thesis Poisson structures of two classical gauge field theories (Maxwell-Klein-Gordon- and Maxwell-Dirac-system) are constructed using the parametrix construction of Green's functions. Parametrices for the Maxwell-Klein-Gordon- and Maxwell-Dirac-system are constructed in Minkowski space and this construction is later generalized to curved space times for the Maxwell-Klein-Gordon-system. With these Green's functions Poisson brackets will be defined as Peierls brackets. Finally non-local, gauge invariant observables, the so-called 'gauge bridges'are constructed. Gauge bridges are the matrix elements of holonomy operators. It is shown, that these emerge from Poisson brackets of local, gauge invariant observables. (orig.)
Refined BPS invariants, Chern-Simons theory, and the quantum dilogarithm
Dimofte, Tudor Dan
In this thesis, we consider two main subjects: the refined BPS invariants of Calabi-Yau threefolds, and three-dimensional Chern-Simons theory with complex gauge group. We study the wall-crossing behavior of refined BPS invariants using a variety of techniques, including a four-dimensional supergravity analysis, statistical-mechanical melting crystal models, and relations to new mathematical invariants. We conjecture an equivalence between refined invariants and the motivic Donaldson-Thomas invariants of Kontsevich and Soibelman. We then consider perturbative Chern-Simons theory with complex gauge group, combining traditional and novel approaches to the theory (including a new state integral model) to obtain exact results for perturbative partition functions. We thus obtain a new class of topological invariants, which are not of finite type, defined in the background of genuinely nonabelian flat connections. The two main topics, BPS invariants and Chern-Simons theory, are connected at both a formal and (we believe) deeper conceptual level by the striking central role that the quantum dilogarithm function plays in each.
Modern Classical Electrodynamics and Electromagnetic Radiation - Vacuum Field Theory Aspects
2011-01-01
The work is devoted to studying some new classical electrodynamics models of interacting charged point particles and related with them physical aspects. Based on the vacuum field theory no-geometry approach, developed in \\cite{BPT,BPT1}, the Lagrangian and Hamiltonian reformulations of some alternative classical electrodynamics models are devised. A problem closely related to the radiation reaction force is analyzed aiming to explain the Wheeler and Feynman reaction radiation mechanism, well ...
A class of exact classical solutions to string theory.
Coley, A A
2002-12-31
We show that the recently obtained class of spacetimes for which all of the scalar curvature invariants vanish (which can be regarded as generalizations of pp-wave spacetimes) are exact solutions in string theory to all perturbative orders in the string tension scale. As a result the spectrum of the theory can be explicitly obtained, and these spacetimes are expected to provide some hints for the study of superstrings on more general backgrounds. Since these Lorentzian spacetimes suffer no quantum corrections to all loop orders they may also offer insights into quantum gravity.
Plasmon mass scale in classical nonequilibrium gauge theory
Lappi, Tuomas
2016-01-01
Classical lattice Yang-Mills calculations provide a good way to understand different nonequilibrium phenomena in nonperturbatively overoccupied systems. Above the Debye scale the classical theory can be matched smoothly to kinetic theory. The aim of this work is to study the limits of this quasiparticle picture by determining the plasmon mass in classical real time Yang-Mills theory on a lattice in 3 spatial dimensions. We compare three methods to determine the plasmon mass: a hard thermal loop expression in terms of the particle distribution, an effective dispersion relation constructed from fields and their time derivatives, and by measuring oscillations between electric and magnetic field modes after artificially introducing a homogeneous color electric field. We find that a version of the dispersion relation that uses electric fields and their time derivatives agrees with the other methods within 50%.
Classical theory of atomic collisions - The first hundred years
Grujić, Petar V.
2012-05-01
Classical calculations of the atomic processes started in 1911 with famous Rutherford's evaluation of the differential cross section for α particles scattered on foil atoms [1]. The success of these calculations was soon overshadowed by the rise of Quantum Mechanics in 1925 and its triumphal success in describing processes at the atomic and subatomic levels. It was generally recognized that the classical approach should be inadequate and it was neglected until 1953, when the famous paper by Gregory Wannier appeared, in which the threshold law for the single ionization cross section behaviour by electron impact was derived. All later calculations and experimental studies confirmed the law derived by purely classical theory. The next step was taken by Ian Percival and collaborators in 60s, who developed a general classical three-body computer code, which was used by many researchers in evaluating various atomic processes like ionization, excitation, detachment, dissociation, etc. Another approach was pursued by Michal Gryzinski from Warsaw, who started a far reaching programme for treating atomic particles and processes as purely classical objects [2]. Though often criticized for overestimating the domain of the classical theory, results of his group were able to match many experimental data. Belgrade group was pursuing the classical approach using both analytical and numerical calculations, studying a number of atomic collisions, in particular near-threshold processes. Riga group, lead by Modris Gailitis [3], contributed considerably to the field, as it was done by Valentin Ostrovsky and coworkers from Sanct Petersbourg, who developed powerful analytical methods within purely classical mechanics [4]. We shall make an overview of these approaches and show some of the remarkable results, which were subsequently confirmed by semiclassical and quantum mechanical calculations, as well as by the experimental evidence. Finally we discuss the theoretical and
Non-classical Measurement Theory: a Framework for Behavioral Sciences
Danilov, V I
2006-01-01
Instances of non-commutativity are pervasive in human behavior. In this paper, we suggest that psychological properties such as attitudes, values, preferences and beliefs may be suitably described in terms of the mathematical formalism of quantum mechanics. We expose the foundations of non-classical measurement theory building on a simple notion of orthospace and ortholattice (logic). Two axioms are formulated and the characteristic state-property duality is derived. A last axiom concerned with the impact of measurements on the state takes us with a leap toward the Hilbert space model of Quantum Mechanics. An application to behavioral sciences is proposed. First, we suggest an interpretation of the axioms and basic properties for human behavior. Then we explore an application to decision theory in an example of preference reversal. We conclude by formulating basic ingredients of a theory of actualized preferences based in non-classical measurement theory.
Spectral and scattering theory for translation invariant models in quantum field theory
DEFF Research Database (Denmark)
Rasmussen, Morten Grud
This thesis is concerned with a large class of massive translation invariant models in quantum field theory, including the Nelson model and the Fröhlich polaron. The models in the class describe a matter particle, e.g. a nucleon or an electron, linearly coupled to a second quantised massive scalar...... of the essential energy-momentum spectrum and either the two-body threshold, if there are no exited isolated mass shells, or the one-body threshold pertaining to the first exited isolated mass shell, if it exists. For the model restricted to the vacuum and one-particle sectors, the absence of singular continuous...... spectrum is proven to hold globally and scattering theory of the model is studied using time-dependent methods, of which the main result is asymptotic completeness....
Classical electromagnetic field theory in the presence of magnetic sources
Chen, W J; Naón, C M; Chen, Wen-Jun; Li, Kang
2001-01-01
Using two new well defined 4-dimensional potential vectors, we formulate the classical Maxwell's field theory in a form which has manifest Lorentz covariance and SO(2) duality symmetry in the presence of magnetic sources. We set up a consistent Lagrangian for the theory. Then from the action principle we get both Maxwell's equation and the equation of motion of a dyon moving in the electro-magnetic field.
Classical Electromagnetic Field Theory in the Presence of Magnetic Sources
Institute of Scientific and Technical Information of China (English)
LI Kang(李康); CHEN Wen-Jun(陈文俊); NAON Carlos M.
2003-01-01
Using two new well-defined four-dimensional potential vectors, we formulate the classical Maxwell field theory in a form which has manifest Lorentz covariance and SO(2) duality symmetry in the presence of magnetic sources.We set up a consistent Lagrangian for the theory. Then from the action principle we obtain both Maxwell's equation and the equation of motion of a dyon moving in the electromagnetic field.
Representational Realism, Closed Theories and the Quantum to Classical Limit
de Ronde, Christian
2016-01-01
In this paper we discuss the representational realist stance as a pluralist ontic approach to inter-theoretic relationships. Our stance stresses the fact that physical theories require the necessary consideration of a conceptual level of discourse which determines and configures the specific field of phenomena discussed by each particular theory. We will criticize the orthodox line of research which has grounded the analysis about QM in two (Bohrian) metaphysical presuppositions -accepted in the present as dogmas that all interpretations must follow. We will also examine how the orthodox project of "bridging the gap" between the quantum and the classical domains has constrained the possibilities of research, producing only a limited set of interpretational problems which only focus in the justification of "classical reality" and exclude the possibility of analyzing the possibilities of non-classical conceptual representations of QM. The representational realist stance introduces two new problems, namely, the ...
Aesthetic Creativity: Insights from Classical Literary Theory on Creative Learning
Hellstrom, Tomas Georg
2011-01-01
This paper addresses the subject of textual creativity by drawing on work done in classical literary theory and criticism, specifically new criticism, structuralism and early poststructuralism. The question of how readers and writers engage creatively with the text is closely related to educational concerns, though they are often thought of as…
Classical Stasis Theory and the Analysis of Public Policy.
Hatch, Gary Layne
In classical Greece, there was a close tie between rhetoric and the practice and theory of public policy. Gradually, however, rhetoric became increasingly concerned with style and literary criticism, while philosophers began to debate political issues apart from the practical affairs of the polis. Because rhetoric provides a model that can still…
Duality and gauge invariance of non-commutative spacetime Podolsky electromagnetic theory
Abreu, Everton M. C.; Fernandes, Rafael L.; Mendes, Albert C. R.; Neto, Jorge Ananias; Neves, Mario, Jr.
2017-01-01
The interest in higher derivative field theories has its origin mainly in their influence concerning the renormalization properties of physical models and to remove ultraviolet divergences. In this paper, we have introduced the non-commutative (NC) version of the Podolsky theory and we investigated the effect of the non-commutativity over its original gauge invariance property. We have demonstrated precisely that the non-commutativity spoiled the primary gauge invariance of the original action under this primary gauge transformation. After that we have used the Noether dualization technique to obtain a dual and gauge invariant action. We have demonstrated that through the introduction of a Stueckelberg field in this NC model, we can also recover the primary gauge invariance. In this way, we have accomplished a comparison between both methods.
The formalism of invariants in scalar-tensor and multiscalar-tensor theories of gravitation
Jarv, Laur; Saal, Margus; Vilson, Ott
2016-01-01
We give a brief summary of the formalism of invariants in general scalar-tensor and multiscalar-tensor gravities without derivative couplings. By rescaling of the metric and reparametrization of the scalar fields, the theory can be presented in different conformal frames and parametrizations. Due to this freedom in transformations, the scalar fields themselves do not carry independent physical meaning (in a generic parametrization). However, there are functions of the scalar fields and their derivatives which remain invariant under the transformations, providing a set of physical variables for the theory. We indicate how to construct such invariants and show how the observables like parametrized post-Newtonian parameters and characteristics of Friedmann-Lemaitre-Robertson-Walker cosmology can be neatly expressed in terms of the invariants.
Probing Hawking and Unruh effects and quantum field theory in curved space by geometric invariants
Capolupo, Antonio
2013-01-01
The presence of noncyclic geometric invariant is revealed in all the phenomena where particle generation from vacuum or vacuum condensates appear. Aharonov--Anandan invariants then can help to study such systems and can represent a new tool to be used in order to provide laboratory evidence of phenomena particulary hard to be detected, such as Hawking and Unruh effects and some features of quantum field theory in curved space simulated by some graphene morphologies. It is finally suggested that a very precise quantum thermometer can be built by exploiting geometric invariants properties.
Whitney smooth families of invariant tori within the reversible context 2 of KAM theory
Sevryuk, Mikhail B.
2016-11-01
We prove a general theorem on the persistence of Whitney C ∞-smooth families of invariant tori in the reversible context 2 of KAM theory. This context refers to the situation where dim Fix G Fix G is the fixed point manifold of the reversing involution G and T is the invariant torus in question. Our result is obtained as a corollary of the theorem by H. W.Broer, M.-C.Ciocci, H.Hanßmann, and A.Vanderbauwhede (2009) concerning quasi-periodic stability of invariant tori with singular "normal" matrices in reversible systems.
Yang-Mills theory in terms of gauge invariant dual variables
Diakonov, D
2002-01-01
Quantum Yang-Mills theory and the Wilson loop can be rewritten identically in terms of local gauge-invariant variables being directly related to the metric of the dual space. In this formulation, one reveals a hidden high local symmetry of the Yang-Mills theory, which mixes up fields with spins up to J=N for the SU(N) gauge group. In the simplest case of the SU(2) group the dual space seems to tend to the de Sitter space in the infrared region. This observation suggests a new mechanism of gauge-invariant mass generation in the Yang-Mills theory.
One loop radiative corrections to the translation-invariant noncommutative Yukawa Theory
Bouchachia, Karim; Hachemane, Mahmoud; Schweda, Manfred
2015-01-01
We elaborate in this paper a translation-invariant model for fermions in 4-dimensional noncommutative Euclidean space. The construction is done on the basis of the renormalizable noncommutative translation-invariant Phi4 theory introduced by R. Gurau et al. We combine our model with the scalar model, in order to study the noncommutative pseudo-scalar Yukawa theory. After we derive the Feynman rules of the theory, we perform an explicit calculation of the quantum corrections at one loop level to the propagators and vertices.
Mozaffar, M R Mohammadi; Sheikh-Jabbari, M M; Vahidinia, M H
2016-01-01
It is established that physical observables in local quantum field theories should be invariant under invertible field redefinitions. It is then expected that this statement should be true for the entanglement entropy and moreover that, via the gauge/gravity correspondence, the recipe for computing entanglement entropy holographically should also be invariant under field redefinitions in the gravity side. We use this fact to fix the recipe for computing holographic entanglement entropy (HEE) for $f(R,R_{\\mu\
Massless and Massive Gauge-Invariant Fields in the Theory of Relativistic Wave Equations
Pletyukhov, V A
2010-01-01
In this work consideration is given to massless and massive gauge-invariant spin 0 and spin 1 fields (particles) within the scope of a theory of the generalized relativistic wave equations with an extended set of the Lorentz group representations. The results obtained may be useful as regards the application of a relativistic wave-equation theory in modern field models.
Theory of Optimal Currency Zones: from Classics until Today
Directory of Open Access Journals (Sweden)
Pinchuk Anastasiya K.
2013-12-01
Full Text Available The article analyses evolution of the theory of optimal currency zones (OCZ, starting from its classical provisions until moder developments. Based on the critical analysis of classical criteria of OCZ, the article develops a scheme of selection of the currency mode by the Robert Mundell theory. It considers achievements of the alternative OCZ theory, the main provisions of which are shown schematically in the form of illustrations of evolution of the theory of optimal currency zones. In the result of analysis of classical criteria of optimal currency zones and generalisation of developments of the new OCZ theory, the article develops a universal algorithm of identification of optimal conditions for an efficient currency zone. Using this algorithm allows identification of a system of quantitative indicators of expediency of regional joining the OCZ, on the basis of which one can build an economic model of an optimal currency zone, which reflects the degree of readiness of any country to join or develop the OCZ. Development of this model is necessary for many countries that face the need to select the currency integration. This model is of special importance for Ukraine, for which it is important to select the course of external integration, since various directions of foreign policy significantly influence efficiency of the domestic economic policy in the country.
Institute of Scientific and Technical Information of China (English)
ZHANG Jia-Lin; YU Hong-Wei
2005-01-01
@@ We show that the velocity and position dispersions of a test particle with a nonzero constant classical velocity undergoing Brownian motion caused by electromagnetic vacuum fluctuations in a space with plane boundaries can be obtained from those of the static case by Lorentz transformation. We explicitly derive the Lorentz transformations relating the dispersions of the two cases and then apply them to the case of the Brownian motion of a test particle with a constant classical velocity parallel to the boundary between two conducting planes. Our results show that the influence of a nonzero initial velocity is negligible for nonrelativistic test particles.
Classical Effective Field Theory and Caged Black Holes
Kol, Barak
2007-01-01
Matched Asymptotic Expansion (MAE) is a useful technique in General Relativity and other fields whenever interaction takes place between physics at two different length scales. Here MAE is argued to be equivalent quite generally to Classical Effective Field Theory (ClEFT) where one (or more) of the zones is replaced by an effective theory whose terms are organized in order of increasing irrelevancy, as demonstrated by Goldberger and Rothstein in a certain gravitational context. The ClEFT perspective has advantages as the procedure is clearer, it allows a representation via Feynman diagrams, and divergences can be regularized and renormalized in standard field theoretic methods. As a side product we obtain a wide class of classical examples of regularization and renormalization, concepts which are usually associated with Quantum Field Theories. We demonstrate these ideas through the thermodynamics of caged black holes, both simplifying the non-rotating case, and computing the rotating case. In particular we ar...
Modern Classical Electrodynamics and Electromagnetic Radiation - Vacuum Field Theory Aspects
Bogolubov, N N
2012-01-01
The work is devoted to studying some new classical electrodynamics models of interacting charged point particles and related with them physical aspects. Based on the vacuum field theory no-geometry approach, developed in \\cite{BPT,BPT1}, the Lagrangian and Hamiltonian reformulations of some alternative classical electrodynamics models are devised. A problem closely related to the radiation reaction force is analyzed aiming to explain the Wheeler and Feynman reaction radiation mechanism, well known as the absorption radiation theory, and strongly dependent on the Mach type interaction of a charged point particle in an ambient vacuum electromagnetic medium. There are discussed some relationships between this problem and the one derived within the context of the vacuum field theory approach. The R. \\ Feynman's \\textquotedblleft heretical\\textquotedblright\\ approach \\cite{Dy1,Dy2} to deriving the Lorentz force based Maxwell electromagnetic equations is also revisited, its complete legacy is argued both by means o...
THE NEW CLASSICAL THEORY AND THE REAL BUSINESS CYCLE MODEL
Directory of Open Access Journals (Sweden)
Oana Simona HUDEA (CARAMAN
2014-11-01
Full Text Available The present paper aims at describing some key elements of the new classical theory-related model, namely the Real Business Cycle, mainly describing the economy from the perspective of a perfectly competitive market, characterised by price, wage and interest rate flexibility. The rendered impulse-response functions, that help us in revealing the capacity of the model variables to return to their steady state under the impact of a structural shock, be it technology or monetary policy oriented, give points to the neutrality of the monetary entity decisions, therefore confirming the well-known classical dichotomy existing between the nominal and the real factors of the economy.
Classic Grounded Theory to Analyse Secondary Data: Reality and Reflections
Directory of Open Access Journals (Sweden)
Lorraine Andrews
2012-06-01
Full Text Available This paper draws on the experiences of two researchers and discusses how they conducted a secondary data analysis using classic grounded theory. The aim of the primary study was to explore first-time parents’ postnatal educational needs. A subset of the data from the primary study (eight transcripts from interviews with fathers was used for the secondary data analysis. The objectives of the secondary data analysis were to identify the challenges of using classic grounded theory with secondary data and to explore whether the re-analysis of primary data using a different methodology would yield a different outcome. Through the process of re-analysis a tentative theory emerged on ‘developing competency as a father’. Challenges encountered during this re-analysis included the small dataset, the pre-framed data, and limited ability for theoretical sampling. This re-analysis proved to be a very useful learning tool for author 1(LA, who was a novice with classic grounded theory.
Kubo, Jisuke
2016-01-01
We assume that the origin of the electroweak (EW) scale is a gauge-invariant scalar-bilinear condensation in a strongly interacting non-abelian gauge sector, which is connected to the standard model via a Higgs portal coupling. The dynamical scale genesis appears as a phase transition at finite temperature, and it can produce a gravitational wave (GW) background in the early Universe. We find that the critical temperature of the scale phase transition lies above that of the EW phase transition and below few $O(100)$ GeV and it is strongly first-order. We calculate the spectrum of the GW background and find the scale phase transition is strong enough that the GW background can be observed by DECIGO.
Energy Technology Data Exchange (ETDEWEB)
Kubo, Jisuke [Institute for Theoretical Physics, Kanazawa University,Kanazawa 920-1192 (Japan); Yamada, Masatoshi [Department of Physics, Kyoto University,Kyoto 606-8502 (Japan); Institut für Theoretische Physik, Universität Heidelberg,Philosophenweg 16, 69120 Heidelberg (Germany)
2016-12-01
We assume that the origin of the electroweak (EW) scale is a gauge-invariant scalar-bilinear condensation in a strongly interacting non-abelian gauge sector, which is connected to the standard model via a Higgs portal coupling. The dynamical scale genesis appears as a phase transition at finite temperature, and it can produce a gravitational wave (GW) background in the early Universe. We find that the critical temperature of the scale phase transition lies above that of the EW phase transition and below few O(100) GeV and it is strongly first-order. We calculate the spectrum of the GW background and find the scale phase transition is strong enough that the GW background can be observed by DECIGO.
Classical field theory on electrodynamics, non-Abelian gauge theories and gravitation
Scheck, Florian
2012-01-01
The book describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary of semi-Riemannian geometry as the framework for the classical field theory of gravitation. The chapter concludes wit...
The First Fundamental Theorem of Invariant Theory for the Orthosymplectic Supergroup
Lehrer, G. I.; Zhang, R. B.
2016-08-01
We give an elementary and explicit proof of the first fundamental theorem of invariant theory for the orthosymplectic supergroup by generalising the geometric method of Atiyah, Bott and Patodi to the supergroup context. We use methods from super-algebraic geometry to convert invariants of the orthosymplectic supergroup into invariants of the corresponding general linear supergroup on a different space. In this way, super Schur-Weyl-Brauer duality is established between the orthosymplectic supergroup of superdimension (m|2n) and the Brauer algebra with parameter m - 2n. The result may be interpreted either in terms of the group scheme OSp(V) over C, where V is a finite dimensional super space, or as a statement about the orthosymplectic Lie supergroup over the infinite dimensional Grassmann algebra {Λ} . We take the latter point of view here, and also state a corresponding theorem for the orthosymplectic Lie superalgebra, which involves an extra invariant generator, the super-Pfaffian.
The First Fundamental Theorem of Invariant Theory for the Orthosymplectic Supergroup
Lehrer, G. I.; Zhang, R. B.
2017-01-01
We give an elementary and explicit proof of the first fundamental theorem of invariant theory for the orthosymplectic supergroup by generalising the geometric method of Atiyah, Bott and Patodi to the supergroup context. We use methods from super-algebraic geometry to convert invariants of the orthosymplectic supergroup into invariants of the corresponding general linear supergroup on a different space. In this way, super Schur-Weyl-Brauer duality is established between the orthosymplectic supergroup of superdimension ( m|2 n) and the Brauer algebra with parameter m - 2 n. The result may be interpreted either in terms of the group scheme OSp( V) over C, where V is a finite dimensional super space, or as a statement about the orthosymplectic Lie supergroup over the infinite dimensional Grassmann algebra {Λ}. We take the latter point of view here, and also state a corresponding theorem for the orthosymplectic Lie superalgebra, which involves an extra invariant generator, the super-Pfaffian.
Modular invariance and (quasi)-Galois symmetry in conformal field theory
Schellekens, Adrian Norbert
1994-01-01
A brief heuristic explanation is given of recent work with Jürgen Fuchs, Beatriz Gato-Rivera and Christoph Schweigert on the construction of modular invariant partition functions from Galois symmetry in conformal field theory. A generalization, which we call quasi-Galois symmetry, is also described. As an application of the latter, the invariants of the exceptional algebras at level g (for example E_8 level 30) expected from conformal embeddings are presented. [Contribution to the Proceedings of the International Symposium on the Theory of Elementary Particles Wendisch-Rietz, August 30 - September 3, 1994
CPT/Lorentz Invariance Violation and Quantum Field Theory
Arias, P; Gamboa-Rios, J; López-Sarrion, J; Méndez, F; Arias, Paola; Das, Ashok; Gamboa, Jorge; Lopez-Sarrion, Justo; Mendez, Fernando
2006-01-01
Analogies between the noncommutative harmonic oscillator and noncommutative fields are analyzed. Following this analogy we construct examples of quantum fields theories with explicit CPT and Lorentz symmetry breaking. Some applications to baryogenesis and neutrino oscillation are also discussed
Quiver Theories for Moduli Spaces of Classical Group Nilpotent Orbits
Hanany, Amihay
2016-01-01
We approach the topic of Classical group nilpotent orbits from the perspective of their moduli spaces, described in terms of Hilbert series and generating functions. We review the established Higgs and Coulomb branch quiver theory constructions for A series nilpotent orbits. We present systematic constructions for BCD series nilpotent orbits on the Higgs branches of quiver theories defined by canonical partitions; this paper collects earlier work into a systematic framework, filling in gaps and providing a complete treatment. We find new Coulomb branch constructions for above minimal nilpotent orbits, including some based upon twisted affine Dynkin diagrams. We also discuss aspects of 3d mirror symmetry between these Higgs and Coulomb branch constructions and explore dualities and other relationships, such as HyperKahler quotients, between quivers. We analyse all Classical group nilpotent orbit moduli spaces up to rank 4 by giving their unrefined Hilbert series and the Highest Weight Generating functions for ...
Conformal Field Theory Correlators from Classical Scalar Field Theory on $AdS_{d+1}$
Mück, W; Mueck, Wolfgang
1998-01-01
We use the correspondence between scalar field theory on $AdS_{d+1}$ and a conformal field theory on $R^d$ to calculate the 3- and 4-point functions of the latter. The classical scalar field theory action is evaluated at tree level.
A New Fuzzy Set Theory Satisfying All Classical Set Formulas
Institute of Scientific and Technical Information of China (English)
Qing-Shi Gao; Xiao-Yu Gao; Yue Hu
2009-01-01
A new fuzzy set theory, C-fuzzy set theory, is introduced in this paper. It is a particular case of the classical set theory and satisfies all formulas of the classical set theory. To add a limitation to C-fuzzy set system, in which all fuzzy sets must be "non-uniform inclusive" to each other, then it forms a family of sub-systems, the Z-fuzzy set family. It can be proved that the Z0-fuzzy set system, one of Z-fuzzy set systems, is equivalent to Zadeh's fuzzy set system. Analysis shows that 1) Zadeh's fuzzy set system defines the relations A = B and A ∈B between two fuzzy sets A and B as "Vu e U,(u A E (u)=μB(U))" and "Au ∈ U, (μA(U) ≤μB(μ))" respectively is inappropriate, because it makes all fuzzy sets be "non-uniformly inclusive"; 2) it is also inappropriate to define two fuzzy sets' union and intersection operations as the max and rain of their grades of membership, because this prevents fuzzy set's ability to correctly reflect different kinds of fuzzy phenomenon in the natural world. Then it has to work around the problem by invent unnatural functions that are hard to understand, such as augmenting max and min for union and intersection to min{a + b, 1} and max{a + b - 1, 0}, but these functions are incorrect on inclusive case. If both pairs of definitions are used together, not only are they unnatural, but also they are still unable to cover all possible set relationships in the natural world; and 3) it is incorrect to define the set complement as 1 -μA(μ), because it can be proved that set complement cannot exist in Zadeh's fuzzy set, and it causes confusion in logic and thinking. And it is seriously mistaken to believe that logics of fuzzy sets necessarily go against classical and normal thinking, logic, and conception. The C-fuzzy set theory proposed in this paper overcomes all of the above errors and shortcomings, and more reasonably reflects fuzzy phenomenon in the natural world. It satisfies all relations, formulas, and operations of the
Semi-Classical field theory as Decoherence Free Subspaces
Varela, Jaime
2014-01-01
We formulate semi-classical field theory as an approximate decoherence-free-subspace of a finite-dimensional quantum-gravity hilbert space. A complementarity construction can be realized as a unitary transformation which changes the decoherence-free-subspace. This can be translated to signify that field theory on a global slice, in certain space-times, is the simultaneous examination of two different superselected sectors of a gauge theory. We posit that a correct course graining procedure of quantum gravity should be WKB states propagating in a curved background in which particles exiting a horizon have imaginary components to their phases. The field theory appears non-unitary, but it is due to the existence of approximate decoherence free sub-spaces. Furthermore, the importance of operator spaces in the course-graining procedure is discussed. We also briefly touch on Firewalls.
Perturbation Theory in Supersymmetric QED: Infrared Divergences and Gauge Invariance
Dine, Michael; Haber, Howard E; Haskins, Laurel Stephenson
2016-01-01
We study some aspects of perturbation theory in $N=1$ supersymmetric abelian gauge theories with massive charged matter. In general gauges, infrared (IR) divergences and nonlocal behavior arise in 1PI diagrams, associated with a $1/k^4$ term in the propagator for the vector superfield. We examine this structure in supersymmetric QED. The IR divergences are gauge-dependent and must cancel in physical quantities like the electron pole mass. We demonstrate that cancellation takes place in a nontrivial way, amounting to a reorganization of the perturbative series from powers of $e^2$ to powers of $e$. We also show how these complications are avoided in cases where a Wilsonian effective action can be defined.
Classical theory of resonant transition radiation in multilayer structures.
Pardo, B; André, J M
2001-01-01
A rigorous classical electromagnetic theory of the transition radiation in finite and infinite multilayer structures is presented. It makes the standard results of thin-film optics, such as the matrix formalism, accountable; it allows thus an exact treatment of the propagation of the waves induced by the electron. This method is applied to the particular case of the periodic structures to treat the resonant transition radiation (RTR). It is noted that the present theory gives, in the hard x-ray domain, results previously published. The reason for this approach is to make the numerical calculations rigorous and easy. The numerical results of our theory are compared to experimental RTR data obtained recently by Yamada et al. [Phys. Rev. A 59, 3673 (1999)] with a nickel-carbon multilayer structure.
Gauge Fixing Invariance and Anti-BRST Symmetry
Varshovi, Amir Abbass
2016-01-01
It is shown that anti-BRST invariance in quantum gauge theories can be considered as the quantized version of the symmetry of classical gauge theories with respect to different gauge fixing mechanisms.
Classical and quantum theory of the massive spin-two field
Koenigstein, Adrian; Giacosa, Francesco; Rischke, Dirk H.
2016-05-01
In this paper, we review classical and quantum field theory of massive non-interacting spin-two fields. We derive the equations of motion and Fierz-Pauli constraints via three different methods: the eigenvalue equations for the Casimir invariants of the Poincaré group, a Lagrangian approach, and a covariant Hamilton formalism. We also present the conserved quantities, the solution of the equations of motion in terms of polarization tensors, and the tree-level propagator. We then discuss canonical quantization by postulating commutation relations for creation and annihilation operators. We express the energy, momentum, and spin operators in terms of the former. As an application, quark-antiquark currents for tensor mesons are presented. In particular, the current for tensor mesons with quantum numbers JPC =2-+ is, to our knowledge, given here for the first time.
Farhi, E; Gutmann, S; Rajagopal, K; Singleton, R; Farhi, E; Goldstone, J; Gutmann, S; Rajagopal, K
1995-01-01
We investigate fermion production in the background of Minkowski space solutions to the equations of motion of SU(2) gauge theory spontaneously broken via the Higgs mechanism. First, we attempt to evaluate the topological charge Q of the solutions. We find that for solutions we cannot define a Lorentz invariant Q as an integral over all space-time. Solutions can profitably be characterized by the (integer-valued) change in Higgs winding number \\Delta N_H. We show that solutions which dissipate at early and late times and which have nonzero \\Delta N_H must have at least the sphaleron energy. We show that if we couple a quantized massive chiral fermion to a classical background given by a solution, the number of fermions produced is \\Delta N_H, and is not related to Q.
Classical Bianchi type I cosmology in K-essence theory
Socorro, J; Espinoza-García, Abraham
2014-01-01
We use one of the simplest forms of the K-essence theory and we apply it to the classical anisotropic Bianchi type I cosmological model, with a barotropic perfect fluid modeling the usual matter content and with cosmological constant. The classical solutions for any but the stiff fluid and without cosmological constant are found in closed form, using a time transformation. We also present the solution whith cosmological constant and some particular values of the barotropic parameter. We present the possible isotropization of the cosmological model, using the ratio between the anisotropic parameters and the volume of the universe and show that this tend to a constant or to zero for different cases. We include also a qualitative analysis of the analog of the Friedmann equation.
The theory of variational hybrid quantum-classical algorithms
McClean, Jarrod R; Babbush, Ryan; Aspuru-Guzik, Alán
2015-01-01
Many quantum algorithms have daunting resource requirements when compared to what is available today. To address this discrepancy, a quantum-classical hybrid optimization scheme known as "the quantum variational eigensolver" was developed with the philosophy that even minimal quantum resources could be made useful when used in conjunction with classical routines. In this work we extend the general theory of this algorithm and suggest algorithmic improvements for practical implementations. Specifically, we develop a variational adiabatic ansatz and explore unitary coupled cluster where we establish a connection from second order unitary coupled cluster to universal gate sets through relaxation of exponential splitting. We introduce the concept of quantum variational error suppression that allows some errors to be suppressed naturally in this algorithm on a pre-threshold quantum device. Additionally, we analyze truncation and correlated sampling in Hamiltonian averaging as ways to reduce the cost of this proced...
Carati, Andrea; Galgani, Luigi
2014-10-01
This paper is a continuation of a recent one in which, apparently for the first time, the existence of polaritons in ionic crystals was proven in a microscopic electrodynamic theory. This was obtained through an explicit computation of the dispersion curves. Here the main further contribution consists in studying electric susceptibility, from which the spectrum can be inferred. We show how susceptibility is obtained by the Green-Kubo methods of Hamiltonian statistical mechanics, and give for it a concrete expression in terms of time-correlation functions. As in the previous paper, here too we work in a completely classical framework, in which the electrodynamic forces acting on the charges are all taken into account, both the retarded forces and the radiation reaction ones. So, in order to apply the methods of statistical mechanics, the system has to be previously reduced to a Hamiltonian one. This is made possible in virtue of two global properties of classical electrodynamics, namely, the Wheeler-Feynman identity and the Ewald resummation properties, the proofs of which were already given for ordered system. The second contribution consists in formulating the theory in a completely general way, so that in principle it applies also to disordered systems such as glasses, or liquids or gases, provided the two general properties mentioned above continue to hold. A first step in this direction is made here by providing a completely general proof of the Wheeler-Feynman identity, which is shown to be the counterpart of a general causality property of classical electrodynamics. Finally it is shown how a line spectrum can appear at all in classical systems, as a counterpart of suitable stability properties of the motions, with a broadening due to a coexistence of chaoticity. The relevance of some recent results of the theory of dynamical systems in this connection is also pointed out.
Gauge-invariant theories of linear response for strongly correlated superconductors
Boyack, Rufus; Anderson, Brandon M.; Wu, Chien-Te; Levin, K.
2016-09-01
We present a diagrammatic theory for determining consistent electromagnetic response functions in strongly correlated fermionic superfluids. While a gauge-invariant electromagnetic response is well understood at the BCS level, a treatment of correlations beyond BCS theory requires extending this theoretical formalism. The challenge in such systems is to maintain gauge invariance, while simultaneously incorporating additional self-energy terms arising from strong correlation effects. Central to our approach is the application of the Ward-Takahashi identity, which introduces collective mode contributions in the response functions and guarantees that the f -sum rule is satisfied. We outline a powerful method, which determines these collective modes in the presence of correlation effects and in a manner compatible with gauge invariance. Since this method is based on fundamental aspects of quantum field theory, the underlying principles are broadly applicable to strongly correlated superfluids. As an illustration of the technique, we apply it to a simple class of theoretical models that contain a frequency-independent order parameter. These models include BCS-BEC crossover theories of the ultracold Fermi gases, along with models specifically associated with the high-Tc cuprates. Finally, as an alternative approach, we contrast with the path integral formalism. Here, the calculation of gauge-invariant response appears more straightforward. However, the collective modes introduced are those of strict BCS theory, without any modification from additional correlations. As the path integral simultaneously addresses electrodynamics and thermodynamics, we emphasize that it should be subjected to a consistency test beyond gauge invariance, namely that of the compressibility sum rule. We show how this sum rule fails in the conventional path integral approach.
Entropy Spectrum of Black Holes of Heterotic String Theory via Adiabatic Invariance
Institute of Scientific and Technical Information of China (English)
Alexis Larra？ aga; Luis Cabarique; Manuel Londo？ o
2012-01-01
Using adiabatic invariance and the Bohr-Sommerfeld quantization rule we investigate the entropy spectroscopy of two black holes of heterotic string theory,the charged GMGHS and the rotating Sen solutions.It is shown that the entropy spectrum is equally spaced in both cases,identically to the spectrum obtained before for Schwarzschild,Reissner-Nordstr?m and Kerr black holes.Since the adiabatic invariance method does not use quasinormal mode analysis,there is no need to impose the small charge or small angular momentum limits and there is no confusion on whether the real part or the imaginary part of the modes is responsible for the entropy spectrum.
Chiral scale and conformal invariance in 2D quantum field theory.
Hofman, Diego M; Strominger, Andrew
2011-10-14
It is well known that a local, unitary Poincaré-invariant 2D quantum field theory with a global scaling symmetry and a discrete non-negative spectrum of scaling dimensions necessarily has both a left and a right local conformal symmetry. In this Letter, we consider a chiral situation beginning with only a left global scaling symmetry and do not assume Lorentz invariance. We find that a left conformal symmetry is still implied, while right translations are enhanced either to a right conformal symmetry or a left U(1) Kac-Moody symmetry.
Gauge Invariant Effective Action in Abelian Chiral Gauge Theory on the Lattice
Suzuki, H
1999-01-01
Lüscher's recent formulation of Abelian chiral gauge theories on the lattice, in the vacuum (or perturbative) sector in infinite lattice volume, is re-interpreted in terms of the lattice covariant regularization. The gauge invariance of the effective action and the integrability of the gauge current in anomaly-free cases become transparent then. The real part of the effective action is simply one-half of that of the Dirac fermion and, when the Dirac operator has proper properties in the continuum limit, the imaginary part in the continuum limit reproduces the $\\eta$-invariant.}
BOOK REVIEW: Classical Solutions in Quantum Field Theory Classical Solutions in Quantum Field Theory
Mann, Robert
2013-02-01
Quantum field theory has evolved from its early beginnings as a tool for understanding the interaction of light with matter into a rather formidable technical paradigm, one that has successfully provided the mathematical underpinnings of all non-gravitational interactions. Over the eight decades since it was first contemplated the methods have become increasingly more streamlined and sophisticated, yielding new insights into our understanding of the subatomic world and our abilities to make clear and precise predictions. Some of the more elegant methods have to do with non-perturbative and semiclassical approaches to the subject. The chief players here are solitons, instantons, and anomalies. Over the past three decades there has been a steady rise in our understanding of these objects and of our ability to calculate their effects and implications for the rest of quantum field theory. This book is a welcome contribution to this subject. In 12 chapters it provides a clear synthesis of the key developments in these subjects at a level accessible to graduate students that have had an introductory course to quantum field theory. In the author's own words it provides both 'a survey and an overview of this field'. The first half of the book concentrates on solitons--kinks, vortices, and magnetic monopoles--and their implications for the subject. The reader is led first through the simplest models in one spatial dimension, into more sophisticated cases that required more advanced topological methods. The author does quite a nice job of introducing the various concepts as required, and beginning students should be able to get a good grasp of the subject directly from the text without having to first go through the primary literature. The middle part of the book deals with the implications of these solitons for both cosmology and for duality. While the cosmological discussion is quite nice, the discussion on BPS solitons, supersymmetry and duality is rather condensed. It is
The Prediction of Item Parameters Based on Classical Test Theory and Latent Trait Theory
Anil, Duygu
2008-01-01
In this study, the prediction power of the item characteristics based on the experts' predictions on conditions try-out practices cannot be applied was examined for item characteristics computed depending on classical test theory and two-parameters logistic model of latent trait theory. The study was carried out on 9914 randomly selected students…
Sprakel, J.H.B.; Leermakers, F.A.M.; Cohen Stuart, M.A.; Besseling, N.A.M.
2008-01-01
A comprehensive theory is proposed that combines classical nucleation and polymer brush theory to describe star-like polymer micelles. With a minimum of adjustable parameters, the model predicts properties such as critical micelle concentrations and micellar size distributions. The validity of the p
Semi-classical quantum theory for cyclotron radiation
Institute of Scientific and Technical Information of China (English)
陈军锋; 邓劲松; 徐毅; 尤峻汉
1997-01-01
A semi-classical quantum theory of the cyclotron radiation of the nonrelativistic thermal electrons in a very strong magnetic field is presented.The basic formulae of the absorption coefficient of cyclotron resonance kv and the absorption (scattering) cross-section of cyclotron resonance σv have been derived under the quadrupole approximation.σv is an important quantity in the study of the "magnetic inverse-Compton scattering".It is shown that σv is greatly larger than the Thomson cross-sectron σT,which is important in discussing the magnetic inverse-Compton scattering of the relativistic electrons in a very strong magnetic field.
Lie Groupoids in Classical Field Theory I: Noether's Theorem
Costa, Bruno T; Pêgas, Luiz Henrique P
2015-01-01
In the two papers of this series, we initiate the development of a new approach to implementing the concept of symmetry in classical field theory, based on replacing Lie groups/algebras by Lie groupoids/algebroids, which are the appropriate mathematical tools to describe local symmetries when gauge transformations are combined with space-time transformations. Here, we outline the basis of the program and, as a first step, show how to (re)formulate Noether's theorem about the connection between symmetries and conservation laws in this approach.
Bulk and boundary invariants for complex topological insulators from K-theory to physics
Prodan, Emil
2016-01-01
This monograph offers an overview of rigorous results on fermionic topological insulators from the complex classes, namely, those without symmetries or with just a chiral symmetry. Particular focus is on the stability of the topological invariants in the presence of strong disorder, on the interplay between the bulk and boundary invariants and on their dependence on magnetic fields. The first part presents motivating examples and the conjectures put forward by the physics community, together with a brief review of the experimental achievements. The second part develops an operator algebraic approach for the study of disordered topological insulators. This leads naturally to use analysis tools from K-theory and non-commutative geometry, such as cyclic cohomology, quantized calculus with Fredholm modules and index pairings. New results include a generalized Streda formula and a proof of the delocalized nature of surface states in topological insulators with non-trivial invariants. The concluding chapter connect...
Nilpotent symmetry invariance in the non-Abelian 1-form gauge theory: Superfield formalism
Indian Academy of Sciences (India)
R P Malik; B P Mandal
2009-03-01
We demonstrate that the nilpotent Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST symmetry invariance of the Lagrangian density of a four (3 + 1)-dimensional (4D) non-Abelian 1-form gauge theory with Dirac fields can be captured within the frame-work of the superfield approach to BRST formalism. The above 4D theory, where there is an explicit coupling between the non-Abelian 1-form gauge field and the Dirac fields, is considered on a (4,2)-dimensional supermanifold, parametrized by the bosonic 4D space-time variables and a pair of Grassmannian variables. We show that the Grassmannian independence of the super-Lagrangian density, expressed in terms of the (4,2)-dimensional superfields, is a clear signature of the presence of the (anti-)BRST invariance in the original 4D theory.
Emergence Of A Classical World From Within Quantum Theory
Poulin, D
2005-01-01
The starting point of this dissertation is that a quantum state represents the observer's knowledge about the system of interest. As it has been pointed out several times by the opponents of this epistemic interpretation, it is difficult to reconcile this point of view with our common notion of “physical reality”, which exists independently of our monitoring, and can be discovered without disturbance. Indeed, if quantum theory is correct, it should apply to classical systems—including measurement devices—as well as to any other system. In this dissertation, we will study the quantum mechanisms responsible for our perception of the world and demonstrate how they lead to the emergence of an operational objective reality from within quantum theory: several observers gathering information through these mechanisms will arrive at a common consensus about the properties of the world. The two mechanisms we study in great detail are the redundant proliferation of information in ...
Light-cone Wilson loop in classical lattice gauge theory
Laine, M
2013-01-01
The transverse broadening of an energetic jet passing through a non-Abelian plasma is believed to be described by the thermal expectation value of a light-cone Wilson loop. In this exploratory study, we measure the light-cone Wilson loop with classical lattice gauge theory simulations. We observe, as suggested by previous studies, that there are strong interactions already at short transverse distances, which may lead to more efficient jet quenching than in leading-order perturbation theory. We also verify that the asymptotics of the Wilson loop do not change qualitatively when crossing the light cone, which supports arguments in the literature that infrared contributions to jet quenching can be studied with dimensionally reduced simulations in the space-like domain. Finally we speculate on possibilities for full four-dimensional lattice studies of the same observable, perhaps by employing shifted boundary conditions in order to simulate ensembles boosted by an imaginary velocity.
Marshaling Resources: A Classic Grounded Theory Study of Online Learners
Directory of Open Access Journals (Sweden)
Barbara Yalof
2014-06-01
Full Text Available Classic grounded theory (CGT was used to identify a main concern of online students in higher education. One of the main impediments to studying online is a sense of isolation and lack of access to support systems as students navigate through complex requirements of their online programs. Hypothetical probability statements illustrate the imbalance between heightened needs of virtual learners and perceived inadequate support provided by educational institutions. The core variable, marshaling resources, explains how peer supports sustain motivation toward successful program completion. Understanding the critical contribution virtual interpersonal networks make towards maximizing resources by group problem solving is a significant aspect of this theory. Keywords: Online learning, e-learning, personal learning networks, peer networks
A Classical Theory of the Anomalous Zeeman Effect
Espinosa, James; Woodyard, James
2010-10-01
Over a hundred years ago, it was discovered that spectral lines were shifted by magnetic fields. Lorentz was able to explain a small set of phenomena that was ironically called the normal Zeeman effect. It took more than twenty years for Lande to arrive at a vector model of the atom to explain the majority of shiftings called the anomalous Zeeman effect. Within a couple of years, Uhlenbeck and Goudsmit introduced the idea of a spinning electron that would give an underlying explanation of the vector model rules. It is generally taught that without the concept of spin there can be no explanation of all the spectral splittings caused by a magnetic field. We will present a purely classical model developed by Woldemar Voigt to describe the most famous anomalous splitting, the sodium D line. In addition, his theory correctly describes the transition from the weak field state to the strong one, called the Paschen-Back effect. We will show how his theory matches well with our classical picture of the atom.
Quiver theories for moduli spaces of classical group nilpotent orbits
Hanany, Amihay; Kalveks, Rudolph
2016-06-01
We approach the topic of Classical group nilpotent orbits from the perspective of the moduli spaces of quivers, described in terms of Hilbert series and generating functions. We review the established Higgs and Coulomb branch quiver theory constructions for A series nilpotent orbits. We present systematic constructions for BCD series nilpotent orbits on the Higgs branches of quiver theories defined by canonical partitions; this paper collects earlier work into a systematic framework, filling in gaps and providing a complete treatment. We find new Coulomb branch constructions for above minimal nilpotent orbits, including some based upon twisted affine Dynkin diagrams. We also discuss aspects of 3 d mirror symmetry between these Higgs and Coulomb branch constructions and explore dualities and other relationships, such as HyperKähler quotients, between quivers. We analyse all Classical group nilpotent orbit moduli spaces up to rank 4 by giving their unrefined Hilbert series and the Highest Weight Generating functions for their decompositions into characters of irreducible representations and/or Hall Littlewood polynomials.
Hernandez-Zapata, Sergio; 10.1007/s10701-010-9413-7
2010-01-01
A completely Lorentz-invariant Bohmian model has been proposed recently for the case of a system of non-interacting spinless particles, obeying Klein-Gordon equations. It is based on a multi-temporal formalism and on the idea of treating the squared norm of the wave function as a space-time probability density. The particle's configurations evolve in space-time in terms of a parameter {\\sigma}, with dimensions of time. In this work this model is further analyzed and extended to the case of an interaction with an external electromagnetic field. The physical meaning of {\\sigma} is explored. Two special situations are studied in depth: (1) the classical limit, where the Einsteinian Mechanics of Special Relativity is recovered and the parameter {\\sigma} is shown to tend to the particle's proper time; and (2) the non-relativistic limit, where it is obtained a model very similar to the usual non-relativistic Bohmian Mechanics but with the time of the frame of reference replaced by {\\sigma} as the dynamical temporal...
Directory of Open Access Journals (Sweden)
Hao Guo
2015-01-01
Full Text Available Recent experimental progress allows for exploring some important physical quantities of ultracold Fermi gases, such as the compressibility, spin susceptibility, viscosity, optical conductivity, and spin diffusivity. Theoretically, these quantities can be evaluated from suitable linear response theories. For BCS superfluid, it has been found that the gauge invariant linear response theories can be fully consistent with some stringent consistency constraints. When the theory is generalized to stronger than BCS regime, one may meet serious difficulties to satisfy the gauge invariance conditions. In this paper, we try to construct density and spin linear response theories which are formally gauge invariant for a Fermi gas undergoing BCS-Bose-Einstein Condensation (BEC crossover, especially below the superfluid transition temperature Tc. We adapt a particular t-matrix approach which is close to the G0G formalism to incorporate noncondensed pairing in the normal state. We explicitly show that the fundamental constraints imposed by the Ward identities and Q-limit Ward identity are indeed satisfied.
Unified Theory of PT and CP Invariant Topological Metals and Nodal Superconductors.
Zhao, Y X; Schnyder, Andreas P; Wang, Z D
2016-04-15
As PT and CP symmetries are fundamental in physics, we establish a unified topological theory of PT and CP invariant metals and nodal superconductors, based on the mathematically rigorous KO theory. Representative models are constructed for all nontrivial topological cases in dimensions d=1, 2, and 3, with their exotic physical meanings being elucidated in detail. Intriguingly, it is found that the topological charges of Fermi surfaces in the bulk determine an exotic direction-dependent distribution of topological subgap modes on the boundaries. Furthermore, by constructing an exact bulk-boundary correspondence, we show that the topological Fermi points of the PT and CP invariant classes can appear as gapless modes on the boundary of topological insulators with a certain type of anisotropic crystalline symmetry.
A Covariant Master Theory for Novel Galilean Invariant Models and Massive Gravity
Gabadadze, Gregory; Khoury, Justin; Pirtskhalava, David; Trodden, Mark
2012-01-01
Coupling the galileons to a curved background has been a tradeoff between maintaining second order equations of motion, maintaining the galilean shift symmetries, and allowing the background metric to be dynamical. We propose a construction which can achieve all three for a novel class of galilean invariant models, by coupling a scalar with the galilean symmetry to a massive graviton. This generalizes the brane construction for galileons, by adding to the brane a dynamical metric, (non-universally) interacting with the galileon field. Alternatively, it can be thought of as an extension of the ghost-free massive gravity, or as a massive graviton-galileon scalar-tensor theory. In the decoupling limit of these theories, new kinds of galileon invariant interactions arise between the scalar and the longitudinal mode of the graviton. These have higher order equations of motion and infinite powers of the field, yet are ghost-free.
Speed addition and closed time cycle in Lorentz-non-invariant theories
Shabad, Anatoly E
2015-01-01
In theories, whose Lorentz invariance is violated by involvement of an external any-rank tensor, we show that the standard relativistic rule still holds true for summing the signal speed, understood as the group velocity of a wave, with the speed of the reference frame. Provided a superluminal signal is available, this observation enables one to arrange a closed time cycle and hence causality violation, notwithstanding the Lorentz noninvariance. Also an optical anisotropy of a moving medium, isotropic at rest, is revealed.
Bianchi type VI1 cosmological model with wet dark fluid in scale invariant theory of gravitation
Mishra, B
2014-01-01
In this paper, we have investigated Bianchi type VIh, II and III cosmological model with wet dark fluid in scale invariant theory of gravity, where the matter field is in the form of perfect fluid and with a time dependent gauge function (Dirac gauge). A non-singular model for the universe filled with disorder radiation is constructed and some physical behaviors of the model are studied for the feasible VIh (h = 1) space-time.
Latfield2: A c++ library for classical lattice field theory
David, Daverio; Bevis, Neil
2015-01-01
latfield2 is a C++ library designed to simplify writing parallel codes for solving partial differen- tial equations, developed for application to classical field theories in particle physics and cosmology. It is a significant rewrite of the latfield framework, moving from a slab domain decomposition to a rod decomposition, where the last two dimension of the lattice are scattered into a two dimensional process grid. Parallelism is implemented using the Message Passing Interface (MPI) standard, and hidden in the basic objects of grid-based simulations: Lattice, Site and Field. It comes with an integrated parallel fast Fourier transform, and I/O server class permitting computation to continue during the writing of large files to disk. latfield2 has been used for production runs on tens of thousands of processor elements, and is expected to be scalable to hundreds of thousands.
Geometry of Lagrangian First-order Classical Field Theories
Echeverría-Enríquez, A; Román-Roy, N; Echeverr\\'ia-Enr\\'iquez, Arturo; Muñoz-Lecanda, Miguel C.; Román-Roy, Narciso
1996-01-01
We construct a lagrangian geometric formulation for first-order field theories using the canonical structures of first-order jet bundles, which are taken as the phase spaces of the systems in consideration. First of all, we construct all the geometric structures associated with a first-order jet bundle and, using them, we develop the lagrangian formalism, defining the canonical forms associated with a lagrangian density and the density of lagrangian energy, obtaining the {\\sl Euler-Lagrange equations} in two equivalent ways: as the result of a variational problem and developing the {\\sl jet field formalism} (which is a formulation more similar to the case of mechanical systems). A statement and proof of Noether's theorem is also given, using the latter formalism. Finally, some classical examples are briefly studied.
Classical mechanics including an introduction to the theory of elasticity
Hentschke, Reinhard
2017-01-01
This textbook teaches classical mechanics as one of the foundations of physics. It describes the mechanical stability and motion in physical systems ranging from the molecular to the galactic scale. Aside from the standard topics of mechanics in the physics curriculum, this book includes an introduction to the theory of elasticity and its use in selected modern engineering applications, e.g. dynamic mechanical analysis of viscoelastic materials. The text also covers many aspects of numerical mechanics, ranging from the solution of ordinary differential equations, including molecular dynamics simulation of many particle systems, to the finite element method. Attendant Mathematica programs or parts thereof are provided in conjunction with selected examples. Numerous links allow the reader to connect to related subjects and research topics. Among others this includes statistical mechanics (separate chapter), quantum mechanics, space flight, galactic dynamics, friction, and vibration spectroscopy. An introductory...
Complex analysis fundamentals of the classical theory of functions
Stalker, John
1998-01-01
This clear, concise introduction to the classical theory of one complex variable is based on the premise that "anything worth doing is worth doing with interesting examples." The content is driven by techniques and examples rather than definitions and theorems. This self-contained monograph is an excellent resource for a self-study guide and should appeal to a broad audience. The only prerequisite is a standard calculus course. The first chapter deals with a beautiful presentation of special functions. . . . The third chapter covers elliptic and modular functions. . . in much more detail, and from a different point of view, than one can find in standard introductory books. . . . For [the] subjects that are omitted, the author has suggested some excellent references for the reader who wants to go through these topics. The book is read easily and with great interest. It can be recommended to both students as a textbook and to mathematicians and physicists as a useful reference. ---Mathematical Reviews Mainly or...
A numerical efficient way to minimize classical density functional theory.
Edelmann, Markus; Roth, Roland
2016-02-21
The minimization of the functional of the grand potential within the framework of classical density functional theory in three spatial dimensions can be numerically very demanding. The Picard iteration, that is often employed, is very simple and robust but can be rather slow. While a number of different algorithms for optimization problems have been suggested, there is still great need for additional strategies. Here, we present an approach based on the limited memory Broyden algorithm that is efficient and relatively simple to implement. We demonstrate the performance of this algorithm with the minimization of an inhomogeneous bulk structure of a fluid with competing interactions. For the problems we studied, we find that the presented algorithm improves performance by roughly a factor of three.
Principles of physics from quantum field theory to classical mechanics
Jun, Ni
2014-01-01
This book starts from a set of common basic principles to establish the formalisms in all areas of fundamental physics, including quantum field theory, quantum mechanics, statistical mechanics, thermodynamics, general relativity, electromagnetic field, and classical mechanics. Instead of the traditional pedagogic way, the author arranges the subjects and formalisms in a logical-sequential way, i.e. all the formulas are derived from the formulas before them. The formalisms are also kept self-contained. Most of the required mathematical tools are also given in the appendices. Although this book covers all the disciplines of fundamental physics, the book is concise and can be treated as an integrated entity. This is consistent with the aphorism that simplicity is beauty, unification is beauty, and thus physics is beauty. The book may be used as an advanced textbook by graduate students. It is also suitable for physicists who wish to have an overview of fundamental physics. Readership: This is an advanced gradua...
Chern-Simons theory on a lattice and a new description of 3-manifolds invariants
Buffenoir, E
1995-01-01
A new approach to the quantization of Chern-Simons theory has been developed in recent papers of the author. It uses a "simulation" of the moduli space of flat connections modulo the gauge group which reveals to be related to a lattice gauge theory based on a quantum group. After a generalization of the formalism of q-deformed gauge theory to the case of root of unity, we compute explicitely the correlation functions associated to Wilson loops (and more generally to graphs) on a surface with punctures, which are the interesting quantity in the study of moduli space. We then give a new description of Chern-Simons three manifolds invariants based on a description in terms of the mapping class group of a surface. At last we introduce a three dimensional lattice gauge theory based on a quantum group which is a lattice regularization of Chern-Simons theory.
Fundamental Elements and Interactions of Nature: A Classical Unification Theory
Directory of Open Access Journals (Sweden)
Tianxi Zhang
2010-04-01
Full Text Available A classical unification theory that completely unifies all the fundamental interactions of nature is developed. First, the nature is suggested to be composed of the following four fundamental elements: mass, radiation, electric charge, and color charge. All known types of matter or particles are a combination of one or more of the four fundamental elements. Photons are radiation; neutrons have only mass; protons have both mass and electric charge; and quarks contain mass, electric charge, and color charge. The nature fundamental interactions are interactions among these nature fundamental elements. Mass and radiation are two forms of real energy. Electric and color charges are considered as two forms of imaginary energy. All the fundamental interactions of nature are therefore unified as a single interaction between complex energies. The interaction between real energies is the gravitational force, which has three types: mass-mass, mass-radiation, and radiation-radiation interactions. Calculating the work done by the mass-radiation interaction on a photon derives the Einsteinian gravitational redshift. Calculating the work done on a photon by the radiation-radiation interaction derives a radiation redshift, which is much smaller than the gravitational redshift. The interaction between imaginary energies is the electromagnetic (between electric charges, weak (between electric and color charges, and strong (between color charges interactions. In addition, we have four imaginary forces between real and imaginary energies, which are mass-electric charge, radiation-electric charge, mass-color charge, and radiation-color charge interactions. Among the four fundamental elements, there are ten (six real and four imaginary fundamental interactions. This classical unification theory deepens our understanding of the nature fundamental elements and interactions, develops a new concept of imaginary energy for electric and color charges, and provides a
Fundamental Elements and Interactions of Nature: A Classical Unification Theory
Directory of Open Access Journals (Sweden)
Zhang T. X.
2010-04-01
Full Text Available A classical unification theory that completely unifies all the fundamental interactions of nature is developed. First, the nature is suggested to be composed of the following four fundamental elements: mass, radiation, electric charge, and color charge. All known types of matter or particles are a combination of one or more of the four fundamental elements. Photons are radiation; neutrons have only mass; protons have both mass and electric charge; and quarks contain mass, electric charge, and color charge. The nature fundamental interactions are interactions among these nature fundamental elements. Mass and radiation are two forms of real energy. Electric and color charges are con- sidered as two forms of imaginary energy. All the fundamental interactions of nature are therefore unified as a single interaction between complex energies. The interac- tion between real energies is the gravitational force, which has three types: mass-mass, mass-radiation, and radiation-radiation interactions. Calculating the work done by the mass-radiation interaction on a photon derives the Einsteinian gravitational redshift. Calculating the work done on a photon by the radiation-radiation interaction derives a radiation redshift, which is much smaller than the gravitational redshift. The interaction between imaginary energies is the electromagnetic (between electric charges, weak (between electric and color charges, and strong (between color charges interactions. In addition, we have four imaginary forces between real and imaginary energies, which are mass-electric charge, radiation-electric charge, mass-color charge, and radiation- color charge interactions. Among the four fundamental elements, there are ten (six real and four imaginary fundamental interactions. This classical unification theory deep- ens our understanding of the nature fundamental elements and interactions, develops a new concept of imaginary energy for electric and color charges, and provides a
On the Classical String Solutions and String/Field Theory Duality
Aleksandrova, D.; Bozhilov, P.
2003-01-01
We classify almost all classical string configurations, considered in the framework of the semi-classical limit of the string/gauge theory duality. Then, we describe a procedure for obtaining the conserved quantities and the exact classical string solutions in general string theory backgrounds, when the string embedding coordinates depend non-linearly on the worldsheet time parameter.
Mimetic discretization of the Abelian Chern-Simons theory and link invariants
Di Bartolo, Cayetano; Leal, Lorenzo
2012-01-01
A mimetic discretization of the Abelian Chern-Simons theory is presented. The study relies on the formulation of a theory of differential forms in the lattice, including a consistent definition of the Hodge duality operation. Explicit expressions for the Gauss Linking Number in the lattice, which correspond to their continuum counterparts are given. A discussion of the discretization of metric structures in the space of transverse vector densities is presented. The study of these metrics could serve to obtain explicit formulae for knot an link invariants in the lattice.
A unifying framework for ghost-free Lorentz-invariant Lagrangian field theories
Li, Wenliang
2015-01-01
We develop a general framework for Lorentz-invariant Lagrangian field theories that leads to second order equations of motion. The key ingredient is the antisymmetric Kronecker delta. Then we reformulate the general ghost-free Lagrangians in the language of differential forms. The absence of higher order equations of motion stems from the basic fact that every exact form is closed. All known ghost-free Lagrangian theories for spin-0, spin-1, spin-2 fields have natural formulations in this framework. We propose new ghost-free Lagrangians, for example, novel nonlinear kinetic terms for graviton.
van Tonder, André
2008-01-01
We revisit the previously unsolved problems of ensuring Lorentz invariance and non-perturbative unitarity in Lee-Wick theories. We base our discussion on an ultraviolet completion of QED by Lee-Wick ghost fields, which is argued to be asymptotically safe. We argue that as long as the state space is based upon a suitable choice of distributions of a type invented by Gel'fand and Shilov, the Lee-Wick ghosts can be eliminated while preserving Lorentz invariance to produce a unitary theory. The method for eliminating ghosts is in principle non-perturbatively well-defined, in contrast with some previous proposals. We also point out a second, independent mechanism for producing a unitary theory, based on a covariant constraint on the maximum four-momentum, which would imply an amusing connection, based on naturalness, between the coupling constant and the hierarchy of scales in the theory. We further emphasize that the resulting theory is causal, and point out some analogies between between the behaviour of Lee-Wic...
A course in mathematical physics 2 classical field theory
Thirring, Walter
1978-01-01
In the past decade the language and methods ofmodern differential geometry have been increasingly used in theoretical physics. What seemed extravagant when this book first appeared 12 years ago, as lecture notes, is now a commonplace. This fact has strengthened my belief that today students of theoretical physics have to learn that language-and the sooner the better. Afterall, they willbe the professors ofthe twenty-first century and it would be absurd if they were to teach then the mathematics of the nineteenth century. Thus for this new edition I did not change the mathematical language. Apart from correcting some mistakes I have only added a section on gauge theories. In the last decade it has become evident that these theories describe fundamental interactions, and on the classical level their structure is suffi cientlyclear to qualify them for the minimum amount ofknowledge required by a theoretician. It is with much regret that I had to refrain from in corporating the interesting developments in Kal...
Invariant Theory for Dispersed Transverse Isotropy: An Efficient Means for Modeling Fiber Splay
Freed, alan D.; Einstein, Daniel R.; Vesely, Ivan
2004-01-01
Most soft tissues possess an oriented architecture of collagen fiber bundles, conferring both anisotropy and nonlinearity to their elastic behavior. Transverse isotropy has often been assumed for a subset of these tissues that have a single macroscopically-identifiable preferred fiber direction. Micro-structural studies, however, suggest that, in some tissues, collagen fibers are approximately normally distributed about a mean preferred fiber direction. Structural constitutive equations that account for this dispersion of fibers have been shown to capture the mechanical complexity of these tissues quite well. Such descriptions, however, are computationally cumbersome for two-dimensional (2D) fiber distributions, let alone for fully three-dimensional (3D) fiber populations. In this paper, we develop a new constitutive law for such tissues, based on a novel invariant theory for dispersed transverse isotropy. The invariant theory is based on a novel closed-form splay invariant that can easily handle 3D fiber populations, and that only requires a single parameter in the 2D case. The model is polyconvex and fits biaxial data for aortic valve tissue as accurately as the standard structural model. Modification of the fiber stress-strain law requires no re-formulation of the constitutive tangent matrix, making the model flexible for different types of soft tissues. Most importantly, the model is computationally expedient in a finite-element analysis.
Vispoel, Walter P; Morris, Carrie A; Kilinc, Murat
2017-01-23
Although widely recognized as a comprehensive framework for representing score reliability, generalizability theory (G-theory), despite its potential benefits, has been used sparingly in reporting of results for measures of individual differences. In this article, we highlight many valuable ways that G-theory can be used to quantify, evaluate, and improve psychometric properties of scores. Our illustrations encompass assessment of overall reliability, percentages of score variation accounted for by individual sources of measurement error, dependability of cut-scores for decision making, estimation of reliability and dependability for changes made to measurement procedures, disattenuation of validity coefficients for measurement error, and linkages of G-theory with classical test theory and structural equation modeling. We also identify computer packages for performing G-theory analyses, most of which can be obtained free of charge, and describe how they compare with regard to data input requirements, ease of use, complexity of designs supported, and output produced. (PsycINFO Database Record
Eta-invariants and anomalies in U(1)-Chern-Simons theory
Jeffrey, Lisa
2010-01-01
This paper studies U(1)-Chern-Simons theory and its relation to a construction of Chris Beasley and Edward Witten. The natural geometric setup here is that of a three-manifold with a Seifert structure. Based on a suggestion of Edward Witten we are led to study the stationary phase approximation of the path integral for U(1)-Chern-Simons theory after one of the three components of the gauge field is decoupled. This gives an alternative formulation of the partition function for U(1)-Chern-Simons theory that is conjecturally equivalent to the usual U(1)-Chern-Simons theory. The goal of this paper is to establish this conjectural equivalence rigorously through appropriate regularization techniques. This approach leads to some rather surprising results and opens the door to studying hypoelliptic operators and their associated eta invariants in a new light.
Raykov, Tenko; Marcoulides, George A.
2016-01-01
The frequently neglected and often misunderstood relationship between classical test theory and item response theory is discussed for the unidimensional case with binary measures and no guessing. It is pointed out that popular item response models can be directly obtained from classical test theory-based models by accounting for the discrete…
Sprakel, Joris; Leermakers, Frans A M; Cohen Stuart, Martien A; Besseling, Nicolaas A M
2008-09-14
A comprehensive theory is proposed that combines classical nucleation and polymer brush theory to describe star-like polymer micelles. With a minimum of adjustable parameters, the model predicts properties such as critical micelle concentrations and micellar size distributions. The validity of the present theory is evidenced in direct comparison to experiments; this revealed that the proportionality constant in the Daoud-Cotton model is of the order of unity and that the star-limit is valid down to relatively short corona chains. Furthermore, we show that the predicted saddle points in the free energy correspond to those solutions that are accessible with self-consistent field methods for self-assembly.
Gauge-invariant theory of two-pion photo- and electro-production off the nucleon
Haberzettl, Helmut; Oh, Yongseok
2012-01-01
A field-theoretical description of the photoproduction of two pions off the nucleon is presented that applies to real as well as virtual photons in the one-photon approximation. The Lorentz-covariant theory is complete at the level of all explicit Faddeev-type three-body final-state mechanisms of dressed interacting hadrons, including those of the nonlinear Dyson-Schwinger type. All electromagnetic currents are constructed to satisfy their respective (generalized) Ward-Takahashi identities and thus satisfy local gauge invariance as a matter of course. The Faddeev-type ordering structure results in a natural expansion of the full two-pion photoproduction current $\\Mpp^\\mu$ in terms of multiple loops that preserve gauge invariance order by order in the number of loops, which in turn lends itself naturally to practical applications of increasing sophistication with increasing number of loops.
A local and BRST-invariant Yang-Mills theory within the Gribov horizon
Capri, M A L; Fiorentini, D; Guimaraes, M S; Justo, I F; Pereira, A D; Mintz, B W; Palhares, L F; Sobreiro, R F; Sorella, S P
2016-01-01
We present a local setup for the recently introduced BRST-invariant formulation of Yang-Mills theories for linear covariant gauges that takes into account the existence of gauge copies \\`a la Gribov and Zwanziger. Through the convenient use of auxiliary fields, including one of the Stueckelberg type, it is shown that both the action and the associated nilpotent BRST operator can be put in local form. Direct consequences of this fully local and BRST-symmetric framework are drawn from its Ward identities: (i) an exact prediction for the longitudinal part of the gluon propagator in linear covariant gauges that is compatible with recent lattice results and (ii) a proof of the gauge-parameter independence of all correlation functions of local BRST-invariant operators.
Loop Variables and Gauge Invariant Exact Renormalization Group Equations for (Open) String Theory
Sathiapalan, B
2012-01-01
An exact renormalization group equation is written down for the world sheet theory describing the bosonic open string in general backgrounds. Loop variable techniques are used to make the equation gauge invariant. This is worked out explicitly up to level 3. The equation is quadratic in the fields and can be viewed as a proposal for a string field theory equation. As in the earlier loop variable approach, the theory has one extra space dimension and mass is obtained by dimensional reduction. Being based on the sigma model RG, it is background independent. It is intriguing that in contrast to BRST string field theory, the gauge transformations are not modified by the interactions up to the level calculated. The interactions can be written in terms of gauge invariant field strengths for the massive higher spin fields and the non zero mass is essential for this. This is reminiscent of Abelian Born-Infeld action (along with derivative corrections) for the massless vector field, which is also written in terms of t...
On covariant Poisson brackets in classical field theory
Energy Technology Data Exchange (ETDEWEB)
Forger, Michael [Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, BR–05315-970 São Paulo, SP (Brazil); Salles, Mário O. [Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, BR–05315-970 São Paulo, SP (Brazil); Centro de Ciências Exatas e da Terra, Universidade Federal do Rio Grande do Norte, Campus Universitário – Lagoa Nova, BR–59078-970 Natal, RN (Brazil)
2015-10-15
How to give a natural geometric definition of a covariant Poisson bracket in classical field theory has for a long time been an open problem—as testified by the extensive literature on “multisymplectic Poisson brackets,” together with the fact that all these proposals suffer from serious defects. On the other hand, the functional approach does provide a good candidate which has come to be known as the Peierls–De Witt bracket and whose construction in a geometrical setting is now well understood. Here, we show how the basic “multisymplectic Poisson bracket” already proposed in the 1970s can be derived from the Peierls–De Witt bracket, applied to a special class of functionals. This relation allows to trace back most (if not all) of the problems encountered in the past to ambiguities (the relation between differential forms on multiphase space and the functionals they define is not one-to-one) and also to the fact that this class of functionals does not form a Poisson subalgebra.
Khrennikov, Andrei
2011-03-01
The idea that quantum randomness can be reduced to randomness of classical fields (fluctuating at time and space scales which are essentially finer than scales approachable in modern quantum experiments) is rather old. Various models have been proposed, e.g., stochastic electrodynamics or the semiclassical model. Recently a new model, so called prequantum classical statistical field theory (PCSFT), was developed. By this model a "quantum system" is just a label for (so to say "prequantum") classical random field. Quantum averages can be represented as classical field averages. Correlations between observables on subsystems of a composite system can be as well represented as classical correlations. In particular, it can be done for entangled systems. Creation of such classical field representation demystifies quantum entanglement. In this paper we show that quantum dynamics (given by Schrödinger's equation) of entangled systems can be represented as the stochastic dynamics of classical random fields. The "effect of entanglement" is produced by classical correlations which were present at the initial moment of time, cf. views of Albert Einstein.
Calculating corrections in F-theory from refined BPS invariants and backreacted geometries
Energy Technology Data Exchange (ETDEWEB)
Poretschkin, Maximilian
2015-07-01
This thesis presents various corrections to F-theory compactifications which rely on the computation of refined Bogomol'nyi-Prasad-Sommerfield (BPS) invariants and the analysis of backreacted geometries. Detailed information about rigid supersymmetric theories in five dimensions is contained in an index counting refined BPS invariants. These BPS states fall into representations of SU(2){sub L} x SU(2){sub R}, the little group in five dimensions, which has an induced action on the cohomology of the moduli space of stable pairs. In the first part of this thesis, we present the computation of refined BPS state multiplicities associated to M-theory compactifications on local Calabi-Yau manifolds whose base is given by a del Pezzo or half K3 surface. For geometries with a toric realization we use an algorithm which is based on the Weierstrass normal form of the mirror geometry. In addition we use the refined holomorphic anomaly equation and the gap condition at the conifold locus in the moduli space in order to perform the direct integration and to fix the holomorphic ambiguity. In a second approach, we use the refined Goettsche formula and the refined modular anomaly equation that govern the (refined) genus expansion of the free energy of the half K3 surface. By this procedure, we compute the refined BPS invariants of the half K3 from which the results of the remaining del Pezzo surfaces are obtained by flop transitions and blow-downs. These calculations also make use of the high symmetry of the del Pezzo surfaces whose homology lattice contains the root lattice of exceptional Lie algebras. In cases where both approaches are applicable, we successfully check the compatibility of these two methods. In the second part of this thesis, we apply the results obtained from the calculation of the refined invariants of the del Pezzo respectively the half K3 surfaces to count non-perturbative objects in F-theory. The first application is given by BPS states of the E
Institute of Scientific and Technical Information of China (English)
Yu Dong-Chuan; Wu Ai-Guo
2006-01-01
A novel La Shalle's invariant set theory (LSIST) based adaptive asymptotic synchronization (LSISAAS) method is proposed to asymptotically synchronize Duffing system with unknown parameters which also are considered as system states. The LSISASS strategy depends on the only information, i.e. one state of the master system. According to the LSIST, the LSISASS method can asymptotically synchronize fully the states of the master system and the unknown system parameters as well. Simulation results also validate that the LSISAAS approach can obtain asymptotic synchronization.
Young, Matthew B
2016-01-01
We introduce a new class of representations of the cohomological Hall algebras of Kontsevich and Soibelman which we call cohomological Hall modules, or CoHM for short. These representations are constructed from self-dual representations of a quiver with contravariant involution $\\sigma$ and provide a mathematical model for the space of BPS states in orientifold string theory. We use the CoHM to define a generalization of cohomological Donaldson-Thomas theory of quivers which allows the quiver representations to have orthogonal and symplectic structure groups. The associated invariants are called orientifold Donaldson-Thomas invariants. We prove the integrality conjecture for orientifold Donaldson-Thomas invariants of $\\sigma$-symmetric quivers. We also formulate precise conjectures regarding the geometric meaning of these invariants and the freeness of the CoHM of a $\\sigma$-symmetric quiver. We prove the freeness conjecture for disjoint union quivers, loop quivers and the affine Dynkin quiver of type $\\widet...
Edery, Ariel; Graham, Noah
2015-05-01
We consider a massless conformally (Weyl) invariant classical action consisting of a magnetic monopole coupled to gravity in an anti-de Sitter background spacetime. We implement quantum corrections and this breaks the conformal (Weyl) symmetry, introduces a length scale via the process of renormalization and leads to the trace anomaly. We calculate the one-loop effective potential and determine from it the vacuum expectation value (VEV). Spontaneous symmetry breaking is radiatively induced a la Coleman-Weinberg and the scalar coupling constant is exchanged for the dimensionful VEV via dimensional transmutation. An important result is that the Ricci scalar of the AdS background spacetimeis determined entirely by the value of the VEV.
Bershtein, Mikhail; Ronzani, Massimiliano; Tanzini, Alessandro
2016-01-01
We show that equivariant Donaldson polynomials of compact toric surfaces can be calculated as residues of suitable combinations of Virasoro conformal blocks, by building on AGT correspondence between N = 2 supersymmetric gauge theories and two-dimensional conformal field theory.
Qian, Xiao-Feng; Howell, John C; Eberly, J H
2015-01-01
The growing recognition that entanglement is not exclusively a quantum property, and does not even originate with Schr\\"odinger's famous remark about it [Proc. Camb. Phil. Soc. {\\bf 31}, 555 (1935)], prompts examination of its role in marking the quantum-classical boundary. We have done this by subjecting correlations of classical optical fields to new Bell-analysis experiments, and report here values of the Bell parameter greater than ${\\cal B} = 2.54$. This is many standard deviations outside the limit ${\\cal B} = 2$ established by the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality [Phys. Rev. Lett. {\\bf 23}, 880 (1969)], in agreement with our theoretical classical prediction, and not far from the Tsirelson limit ${\\cal B} = 2.828...$. These results cast a new light on the standard quantum-classical boundary description, and suggest a reinterpretation of it.
Cabra, D C; Rossini, L; Schaposnik, F A; Fradkin, Eduardo
1995-01-01
We discuss the behavior of theories of fermions coupled to Chern-Simons gauge fields with a non-abelian gauge group in three dimensions and at finite temperature. Using non-perturbative arguments and gauge invariance, and in contradiction with perturbative results, we show that the coefficient of the Chern-Simons term of the effective actions for the gauge fields at finite temperature can be {\\it at most} an integer function of the temperature. This is in a sense a generalized no-renormalization theorem. We also discuss the case of abelian theories and give indications that a similar condition should hold there too. We discuss consequences of our results to the thermodynamics of anyon superfluids and fractional quantum Hall systems.
Invariant exchange perturbation theory for multicenter systems: Time-dependent perturbations
Energy Technology Data Exchange (ETDEWEB)
Orlenko, E. V., E-mail: eorlenko@mail.ru; Evstafev, A. V.; Orlenko, F. E. [St. Petersburg State Technical University (Russian Federation)
2015-02-15
A formalism of exchange perturbation theory (EPT) is developed for the case of interactions that explicitly depend on time. Corrections to the wave function obtained in any order of perturbation theory and represented in an invariant form include exchange contributions due to intercenter electron permutations in complex multicenter systems. For collisions of atomic systems with an arbitrary type of interaction, general expressions are obtained for the transfer (T) and scattering (S) matrices in which intercenter electron permutations between overlapping nonorthogonal states belonging to different centers (atoms) are consistently taken into account. The problem of collision of alpha particles with lithium atoms accompanied by the redistribution of electrons between centers is considered. The differential and total charge-exchange cross sections of lithium are calculated.
Apparently non-invariant terms of nonlinear sigma models in lattice perturbation theory
Harada, Koji; Kubo, Hirofumi; Yamamoto, Yuki
2009-01-01
Apparently non-invariant terms (ANTs) which appear in loop diagrams for nonlinear sigma models (NLSs) are revisited in lattice perturbation theory. The calculations have been done mostly with dimensional regularization so far. In order to establish that the existence of ANTs is independent of the regularization scheme, and of the potential ambiguities in the definition of the Jacobian of the change of integration variables from group elements to "pion" fields, we employ lattice regularization, in which everything (including the Jacobian) is well-defined. We show explicitly that lattice perturbation theory produces ANTs in the four-point functions of the "pion" fields at one-loop and the Jacobian does not play an important role in generating ANTs.
A reappraisal of classical archetype theory and its implications for theory and practice.
Merchant, John
2009-06-01
This paper begins with an overview of contemporary approaches to archetype theory and notes the radical nature of certain deductions. Some argue that there is no 'archetype-as-such' as a pre-existing entity at the core of a complex driving its formation whilst the findings of current neuroscience are calling into question one very thing on which the classical theory is built--innatism. Knox's argument for image schemas raises the question as to the extent to which archetypes can be conceived in any preformationist sense. The question is then posed--to what extent can Jung's classical theory of archetypes be read in light of these current models? The case examples Jung uses to evidence the existence of archetypes, his explications of synchronicity and his own Philemon experience are then reappraised. The conclusion is drawn that it is difficult to evidence the existence of autonomous archetypes unrelated to personal affective experience. Not only would this be expected by emergent/developmental models of archetype but it can explain many of Jung's disjunctive statements about archetype constellation; the difficulties in separating personal and collective psychic content and Jung's apparent Lamarckianism. The implications of these models for theory, clinical practice and analyst training are then offered for discussion.
Multi-Boundary Entanglement in Chern-Simons Theory and Link Invariants
Balasubramanian, Vijay; Leigh, Robert G; Parrikar, Onkar
2016-01-01
We consider Chern-Simons theory for gauge group $G$ at level $k$ on 3-manifolds $M_n$ with boundary consisting of $n$ topologically linked tori. The Euclidean path integral on $M_n$ defines a quantum state on the boundary, in the $n$-fold tensor product of the torus Hilbert space. We focus on the case where $M_n$ is the link-complement of some $n$-component link inside the three-sphere $S^3$. The entanglement entropies of the resulting states define new, framing-independent link invariants which are sensitive to the topology of the chosen link. For the Abelian theory at level $k$ ($G= U(1)_k$) we give a general formula for the entanglement entropy associated to an arbitrary $(m|n-m)$ partition of a generic $n$-component link into sub-links. The formula involves the number of solutions to certain Diophantine equations with coefficients related to the Gauss linking numbers (mod $k$) between the two sublinks. This formula connects simple concepts in quantum information theory, knot theory, and number theory, and...
Sylvester and algebraic invariant theory%西尔维斯特与代数不变量理论
Institute of Scientific and Technical Information of China (English)
金英姬; 白宏刚
2013-01-01
文中利用文献研读与历史分析法,系统研究和探讨了西尔维斯特(James Joseph Sylvester,1814-1897)创立代数不变量理论的相关思想及其贡献:西尔维斯特建立了代数不变量理论的学科语言；发明了计算不变量的一般方法——复合换位法；引进微分算子,建立了不变量零化子理论；尝试利用施图姆函数的合冲关系解决不变量的合冲问题；证明了凯莱定理.西尔维斯特的工作奠定了代数不变量的理论基础,反映了19世纪英国不变量理论研究的主要轨迹及特点.%In this paper,by using the method of the literature review and historic analysis,the thought and contribution of the algebria invariant theory are systematically investigated and discussed,which was found by Sylvester (James Joseph Sylvester,1814-1897):the language of the algebria invariant theory was established by Sylvester,the general method of calculating the invariants-Compound Commutants Method was devised,the theory of the invariant annihilator was established by introducing the differential operators,the syzygy problems of the invariants was attempt to solve by using the syzygetic relations of Strurm functions,Cayley's theorem was proved.Sylvester's work laid the foundation of the algebria invariant theory,and reflected the main research track and feature of the British algebria invariant theory in the 19th century.
Dressing the Post-Newtonian two-body problem and Classical Effective Field Theory
Kol, Barak
2009-01-01
We apply a dressed perturbation theory to better organize and economize the computation of high orders of the 2-body effective action of an inspiralling Post-Newtonian gravitating binary. We use the effective field theory approach with the non-relativistic field decomposition (NRG fields). For that purpose we develop quite generally the dressing theory of a non-linear classical field theory coupled to point-like sources. We introduce dressed charges and propagators, but unlike the quantum theory there are no dressed bulk vertices. The dressed quantities are found to obey recursive integral equations which succinctly encode parts of the diagrammatic expansion, and are the classical version of the Schwinger-Dyson equations. Actually, the classical equations are somewhat stronger since they involve only finitely many quantities, unlike the quantum theory. Classical diagrams are shown to factorize exactly when they contain non-linear world-line vertices, and we classify all the possible topologies of irreducible ...
Surana, K. S.; Joy, A. D.; Reddy, J. N.
2017-03-01
This paper presents a non-classical continuum theory in Lagrangian description for solids in which the conservation and the balance laws are derived by incorporating both the internal rotations arising from the Jacobian of deformation and the rotations of Cosserat theories at a material point. In particular, in this non-classical continuum theory, we have (i) the usual displacements ( ±b \\varvec{u}) and (ii) three internal rotations ({}_i ±b \\varvec{Θ}) about the axes of a triad whose axes are parallel to the x-frame arising from the Jacobian of deformation (which are completely defined by the skew-symmetric part of the Jacobian of deformation), and (iii) three additional rotations ({}_e ±b \\varvec{Θ}) about the axes of the same triad located at each material point as additional three degrees of freedom referred to as Cosserat rotations. This gives rise to ±b \\varvec{u} and {}_e ±b \\varvec{{Θ} as six degrees of freedom at a material point. The internal rotations ({}_i ±b \\varvec{Θ}), often neglected in classical continuum mechanics, exist in all deforming solid continua as these are due to Jacobian of deformation. When the internal rotations {}_i ±b \\varvec{Θ} are resisted by the deforming matter, conjugate moment tensor arises that together with {}_i ±b \\varvec{Θ} may result in energy storage and/or dissipation, which must be accounted for in the conservation and the balance laws. The Cosserat rotations {}_e ±b \\varvec{Θ} also result in conjugate moment tensor which, together with {}_e ±b \\varvec{Θ}, may also result in energy storage and/or dissipation. The main focus of the paper is a consistent derivation of conservation and balance laws that incorporate aforementioned physics and associated constitutive theories for thermoelastic solids. The mathematical model derived here has closure, and the constitutive theories derived using two alternate approaches are in agreement with each other as well as with the condition resulting from the
The supersymmetry method for chiral random matrix theory with arbitrary rotation-invariant weights
Kaymak, Vural; Kieburg, Mario; Guhr, Thomas
2014-07-01
In the past few years, the supersymmetry method has been generalized to real symmetric, Hermitian, and Hermitian self-dual random matrices drawn from ensembles invariant under the orthogonal, unitary, and unitary symplectic groups, respectively. We extend this supersymmetry approach to chiral random matrix theory invariant under the three chiral unitary groups in a unifying way. Thereby we generalize a projection formula providing a direct link and, hence, a ‘short cut’ between the probability density in ordinary space and that in superspace. We emphasize that this point was one of the main problems and shortcomings of the supersymmetry method, since only implicit dualities between ordinary space and superspace were known before. To provide examples, we apply this approach to the calculation of the supersymmetric analogue of a Lorentzian (Cauchy) ensemble and an ensemble with a quartic potential. Moreover, we consider the partially quenched partition function of the three chiral Gaussian ensembles corresponding to four-dimensional continuum quantum chromodynamics. We identify a natural splitting of the chiral Lagrangian in its lowest order into a part for the physical mesons and a part associated with source terms generating the observables, e.g. the level density of the Dirac operator.
A critical experimental study of the classical tactile threshold theory
Directory of Open Access Journals (Sweden)
Medina Leonel E
2010-06-01
Full Text Available Abstract Background The tactile sense is being used in a variety of applications involving tactile human-machine interfaces. In a significant number of publications the classical threshold concept plays a central role in modelling and explaining psychophysical experimental results such as in stochastic resonance (SR phenomena. In SR, noise enhances detection of sub-threshold stimuli and the phenomenon is explained stating that the required amplitude to exceed the sensory threshold barrier can be reached by adding noise to a sub-threshold stimulus. We designed an experiment to test the validity of the classical vibrotactile threshold. Using a second choice experiment, we show that individuals can order sensorial events below the level known as the classical threshold. If the observer's sensorial system is not activated by stimuli below the threshold, then a second choice could not be above the chance level. Nevertheless, our experimental results are above that chance level contradicting the definition of the classical tactile threshold. Results We performed a three alternative forced choice detection experiment on 6 subjects asking them first and second choices. In each trial, only one of the intervals contained a stimulus and the others contained only noise. According to the classical threshold assumptions, a correct second choice response corresponds to a guess attempt with a statistical frequency of 50%. Results show an average of 67.35% (STD = 1.41% for the second choice response that is not explained by the classical threshold definition. Additionally, for low stimulus amplitudes, second choice correct detection is above chance level for any detectability level. Conclusions Using a second choice experiment, we show that individuals can order sensorial events below the level known as a classical threshold. If the observer's sensorial system is not activated by stimuli below the threshold, then a second choice could not be above the chance
One-loop divergences in chiral perturbation theory and right-invariant metrics on SU(3)
Energy Technology Data Exchange (ETDEWEB)
Esposito-Farese, G. (Centre National de la Recherche Scientifique, 13 - Marseille (France). Centre de Physique Theorique)
1991-04-01
In the framework of chiral perturbation theory, we compute the one-loop divergences of the effective Lagrangian describing strong and non-leptonic weak interactions of pseudoscalar mesons. We use the background field method and the heat-kernel expansion, and underline the geometrical meaning of the different terms, showing how the right-invariance of the metrics on SU(3) allows to clarify and simplify the calculations. Our results are given in terms of a minimal set of independent counterterms, and shorten previous ones of the literature, in the particular case where the electromagnetic field is the only external source which is considered. We also show that a geometrical construction of the effective Lagrangian at order O(p{sup 4}) allows to derive some relations between the finite parts of the coupling constants. These relations do not depend on the scale {mu} used to renormalize. (orig.).
How some infinities cause problems in classical physical theories
Atkinson, David; Peijnenburg, Jeanne; Allo, P.; van Kerhove, B.
2014-01-01
In this paper we review a 1992 excursion of Jean Paul Van Bendegem into physics, ‘How Infinities Cause Problems in Classical Physical Theories’, in the light of two later models concerning colliding balls, of Pérez Laraudogoitia and of Alper and Bridger, respectively. We show that Van Bendegem antic
Homology of classical groups and K-theory
Mirzaii, B.
2004-01-01
The study of the homology groups of classical group over a ring R with coefficient A, where A is a commutative ring with trivial group action, seems important, notably because of their close relation to algebraic and Hermitian Ktheory and their appearance in the study of scissors congruence of polyh
On the concept of Bell’s local causality in local classical and quantum theory
Energy Technology Data Exchange (ETDEWEB)
Hofer-Szabó, Gábor, E-mail: szabo.gabor@btk.mta.hu [Research Center for the Humanities, Budapest (Hungary); Vecsernyés, Péter, E-mail: vecsernyes.peter@wigner.mta.hu [Wigner Research Centre for Physics, Budapest (Hungary)
2015-03-15
The aim of this paper is to implement Bell’s notion of local causality into a framework, called local physical theory. This framework, based on the axioms of algebraic field theory, is broad enough to integrate both probabilistic and spatiotemporal concepts and also classical and quantum theories. Bell’s original idea of local causality will arise as the classical case of our definition. Classifying local physical theories by whether they obey local primitive causality, a property rendering the dynamics of the theory causal, we then investigate what is needed for a local physical theory to be locally causal. Finally, comparing local causality with the common cause principles and relating both to the Bell inequalities we find a nice parallelism: Bell inequalities cannot be derived neither from local causality nor from a common cause unless the local physical theory is classical or the common cause is commuting, respectively.
Topological sectors and gauge invariance in massive vector-tensor theories in D $\\geq$ 4
Arias, P J
1996-01-01
A family of local equivalent models is considered. They can be taken as a generalization to d+1 dimensions of the Topological Massive and ``Self-dual'' model in 2+1 dimensions. The corresponding 3+1 models are analized in detail. It is shown that one model can be seen as a gauge fixed version of the other, and their space of classical solutions differs in a topological sector represented by the classical solutions of a pure BF model. The topological sector can be gauged out on cohomologically trivial base manifolds but on general settings it may be responsible of the difference in the long distance behaviour of the models. The presence of this topological sector appears explicitly in the partition function of the theories. The generalization of this models to higher dimensions is shown to be straightfoward.
Chern-Simons Invariants of Torus Knots and Links
Stevan, Sébastien
2010-01-01
We compute the vacuum expectation values of torus knot operators in Chern-Simons theory, and we obtain explicit formulae for all classical gauge groups and for arbitrary representations. We reproduce a known formula for the HOMFLY invariants of torus links and we obtain an analogous formula for Kauffman invariants. We also derive a formula for cable knots. We use our results to test a recently proposed conjecture that relates HOMFLY and Kauffman invariants.
Theory of elites in classical and contemporary political sociology
Pavlović, Vukašin
2011-01-01
The text consists of three parts. The first one analyses classical concepts of elites in the works of Gaetano Mosca, Vilfredo Pareto and Robert Michels. The second part presents and analyses new concepts of elites given in the works by Karl Mannheim, Joseph Schumpeter, James Burnham, Milovan Đilas, Wright Mills, Tom Bottomore, John Kenneth Galbraith, Raymond Aron. The third, concluding part, considers the relation between democracy and elitism.
Energy Technology Data Exchange (ETDEWEB)
French, Doug [School of Nuclear Engineering, Purdue University, West Lafayette, IN 47907 (United States)], E-mail: french@purdue.edu; Huang Zun; Pao, H.-Y.; Jovanovic, Igor [School of Nuclear Engineering, Purdue University, West Lafayette, IN 47907 (United States)
2009-03-02
A quantum phase amplifier operated in the spatial domain can improve the signal-to-noise ratio in imaging beyond the classical limit. The scaling of the signal-to-noise ratio with the gain of the quantum phase amplifier is derived from classical information theory.
Lange, Elizabeth
2015-01-01
This article argues that sociology has been a foundational discipline for the field of adult education, but it has been largely implicit, until recently. This article contextualizes classical theories of sociology within contemporary critiques, reviews the historical roots of sociology and then briefly introduces the classical theories…
Classical Kinetic Theory of Landau Damping for Self-interacting Scalar Fields in the Broken Phase
1998-01-01
The classical kinetic theory of one-component self-interacting scalar fields is formulated in the broken symmetry phase and applied to the phenomenon of Landau damping. The domain of validity of the classical approach is found by comparing with the result of a 1-loop quantum calculation.
Quantum Electrodynamics Basis of Classical-Field High-Harmonic Generation Theory
Institute of Scientific and Technical Information of China (English)
王兵兵; 高靓辉; 傅盘铭; 郭东升; R. R. Freeman
2001-01-01
From the nonperturbative quantum electrodynamics theory, we derive the Landau-Dykhne formula which represents the quantum-mechanical formulation of the three-step model. These studies provide a basis for the classical-field approaches to high-order harmonic generation and justify some assumptions used in classical-field modelling.
Classical conformality in the Standard Model from Coleman’s theory
Kawana, Kiyoharu
2016-09-01
The classical conformality (CC) is one of the possible candidates for explaining the gauge hierarchy of the Standard Model (SM). We show that it is naturally obtained from the Coleman’s theory on baby universe.
Levnajić, Zoran; Mezić, Igor
2010-09-01
We present a computational study of a visualization method for invariant sets based on ergodic partition theory, first proposed by Mezić (Ph.D. thesis, Caltech, 1994) and Mezić and Wiggins [Chaos 9, 213 (1999)]. The algorithms for computation of the time averages of observables on phase space are developed and used to provide an approximation of the ergodic partition of the phase space. We term the graphical representation of this approximation--based on time averages of observables--a mesochronic plot (from Greek: meso--mean, chronos--time). The method is useful for identifying low-dimensional projections (e.g., two-dimensional slices) of invariant structures in phase spaces of dimensionality bigger than two. We also introduce the concept of the ergodic quotient space, obtained by assigning a point to every ergodic set, and provide an embedding method whose graphical representation we call the mesochronic scatter plot. We use the Chirikov standard map as a well-known and dynamically rich example in order to illustrate the implementation of our methods. In addition, we expose applications to other higher dimensional maps such as the Froéschle map for which we utilize our methods to analyze merging of resonances and, the three-dimensional extended standard map for which we study the conjecture on its ergodicity [I. Mezić, Physica D 154, 51 (2001)]. We extend the study in our next paper [Z. Levnajić and I. Mezić, e-print arXiv:0808.2182] by investigating the visualization of periodic sets using harmonic time averages. Both of these methods are related to eigenspace structure of the Koopman operator [I. Mezić and A. Banaszuk, Physica D 197, 101 (2004)].
Branco, António Horta; Costa, Francisco
2005-01-01
This technical report collects the extended abstracts selected for the Workshop on Binding Theory and Invariants in Anaphoric Relations, hosted by the HPSG'2005 Conference (University of Lisbon, August 22, 2005 - http://bindingwksp.di.fc.ul.pt/) by the corresponding program committee
Directory of Open Access Journals (Sweden)
Sargsyan S.H.
2014-03-01
Full Text Available In the present paper, the system of equations of three-dimensional micropolar theory of elasticity, written down for thin shell as singularly perturbed with small geometric parameter system, is analyzed asymptotically: the internal iteration process and boundary layers are constructed, their interaction is studied, boundary conditions are obtained for each of them. Then, the main specific properties of the asymptotic solution accepting as hypotheses, general applied theory of micropolar elastic thin shells is constructed and it is shown that the constructed theory is asymptotically correct. Passing from the micropolar theory of thin shells to the classical theory, it is shown, that this applied classical theory of thin shells, when transverse shifts are taken into account, is asymptotically correct theory in relation to the other corrected theories of thin shells.
Introduction of a Classical Level in Quantum Theory
Prosperi, G. M.
2016-11-01
In an old paper of our group in Milano a formalism was introduced for the continuous monitoring of a system during a certain interval of time in the framework of a somewhat generalized approach to quantum mechanics (QM). The outcome was a distribution of probability on the space of all the possible continuous histories of a set of quantities to be considered as a kind of coarse grained approximation to some ordinary quantum observables commuting or not. In fact the main aim was the introduction of a classical level in the context of QM, treating formally a set of basic quantities, to be considered as beables in the sense of Bell, as continuously taken under observation. However the effect of such assumption was a permanent modification of the Liouville-von Neumann equation for the statistical operator by the introduction of a dissipative term which is in conflict with basic conservation rules in all reasonable models we had considered. Difficulties were even encountered for a relativistic extension of the formalism. In this paper I propose a modified version of the original formalism which seems to overcome both difficulties. First I study the simple models of an harmonic oscillator and a free scalar field in which a coarse grain position and a coarse grained field respectively are treated as beables. Then I consider the more realistic case of spinor electrodynamics in which only certain coarse grained electric and magnetic fields are introduced as classical variables and no matter related quantities.
Anthropology and social theory: renewing dialogue via the classics
DEFF Research Database (Denmark)
Thomassen, Bjørn
2011-01-01
Agnes Horvath, Bjørn Thomassen, & Dr Harald Wydra, editors of the Journal,International Political Anthropology “Anthropology and social theory: renewing dialogue via the classics” This paper argues that anthropology may represent a perspective from where social theory can renew itself. The presen......Agnes Horvath, Bjørn Thomassen, & Dr Harald Wydra, editors of the Journal,International Political Anthropology “Anthropology and social theory: renewing dialogue via the classics” This paper argues that anthropology may represent a perspective from where social theory can renew itself....... The presentation therefore inserts itself within the history of a long conversation between anthropology and social theory. This discussion goes back at least to the Durkhemian school which saw the study of modern and "archaic" cultures as part and parcel of the same project. However, the disciplines of sociology...... with anthropology via the "cultural turn". Yet this elevated status of anthropology and its method has involved almost no engagement with the theoretical luggage found within the discipline of anthropology.Our premise is that the modern world may indeed not be so unique in all its features, and that it therefore...
A course in mathematical physics 1 and 2 classical dynamical systems and classical field theory
Thirring, Walter
1992-01-01
The last decade has seen a considerable renaissance in the realm of classical dynamical systems, and many things that may have appeared mathematically overly sophisticated at the time of the first appearance of this textbook have since become the everyday tools of working physicists. This new edition is intended to take this development into account. I have also tried to make the book more readable and to eradicate errors. Since the first edition already contained plenty of material for a one semester course, new material was added only when some of the original could be dropped or simplified. Even so, it was necessary to expand the chap ter with the proof of the K-A-M Theorem to make allowances for the cur rent trend in physics. This involved not only the use of more refined mathe matical tools, but also a reevaluation of the word "fundamental. " What was earlier dismissed as a grubby calculation is now seen as the consequence of a deep principle. Even Kepler's laws, which determine the radii of the ...
Quantization of light energy directly from classical electromagnetic theory in vacuum
Institute of Scientific and Technical Information of China (English)
She Wei-Long
2005-01-01
It is currently believed that light quantum or the quantization of light energy is beyond classical physics, and the picture of wave-particle duality, which was criticized by Einstein but has attracted a number of experimental researches, is necessary for the description of light. It is shown in this paper, however, that the quantization of light energy in vacuum, which is the same as that in quantum electrodynamics, can be derived directly from the classical electromagnetic theory through the consideration of statistics based on classical physics. Therefore, the quantization of energy is an intrinsic property of light as a classical electromagnetic wave and has no need of being related to particles.
Classical versus Keynesian theory of unemployment : an approach to the Spanish labor market
Alonso Rodríguez, Rubén
2015-01-01
In the last decade the unemployment skyrocketed defining a dramatic landscape for the Spanish economy. In order to understand the root causes, I have revisited two theories widely extended in labor economics: The Classical Theory of Unemployment and the Keynesian Theory of Unemployment. Despite both conceptions are well known and supported by academic literature, in the Spanish case as in many other countries is still unclear what theory better adjust to reality. To solve this lack of clearne...
k-Cosymplectic Classical Field Theories: Tulczyjew and Skinner-Rusk Formulations
Rey, Angel M.; Román-Roy, Narciso; Salgado, Modesto; Vilariño, Silvia
2012-06-01
The k-cosymplectic Lagrangian and Hamiltonian formalisms of first-order classical field theories are reviewed and completed. In particular, they are stated for singular and almost-regular systems. Subsequently, several alternative formulations for k-cosymplectic first-order field theories are developed: First, generalizing the construction of Tulczyjew for mechanics, we give a new interpretation of the classical field equations. Second, the Lagrangian and Hamiltonian formalisms are unified by giving an extension of the Skinner-Rusk formulation on classical mechanics.
New views on classical and quantum Brans-Dicke theory
Fabris, Júlio C; Rodrigues, Davi C; Almeida, Carla R; Piattella, Oliver F
2016-01-01
The Brans-Dicke action is one of the most natural extensions of the Einstein-Hilbert action. It is based on the introduction of a fundamental scalar field that effectively incorporates a dynamics to the gravitational coupling $G$. In spite of the diverse motivations and the rich phenomenology that comes from its solutions, Solar System tests impose strong constraints on the Brans-Dicke theory, rendering it indistinguishable from General Relativity. In the present text, new perspectives for the Brans-Dicke theory are presented, based on the possibility that the scalar field presented in the BD theory can be external, as well as on the applications to black hole physics and the primordial universe.
THE CONCEPT OF INTERNATIONAL TRADE AND MAIN CLASSIC THEORIES
Directory of Open Access Journals (Sweden)
Elena Ramona TERZEA
2016-07-01
Full Text Available Taking into account the major impact that international trade has on the economy and on the people’s lives, and considering its effects on the economic growth, the foreign commerce has to be well understood so that the commercial policies have to be well elaborated, implemented and followed. The theories of international trade are extremely important in order to determine the flows, but especially in the anticipation of the evolution of the forces that influences its dymanic. The theories regarding the foreign trade are used also by the big companies, by their managers, in their attempt to identify the most advantageous strategies of internationalizations, on the most promising markets.
Invariance of the Noether charge
Silagadze, Z K
2016-01-01
Surprisingly, an interesting property of the Noether charge that it is by itself invariant under the corresponding symmetry transformation is never discussed in quantum field theory or classical mechanics textbooks we have checked. This property is also almost never mentioned in articles devoted to Noether's theorem. Nevertheless, to prove this property in the context of Lagrangian formalism is not quite trivial and the proof, outlined in this article, can constitute an useful and interesting exercise for students.
Foundations of the classical theory of partial differential equations
Egorov, Yu V
1998-01-01
From the reviews of the first printing, published as volume 30 of the Encyclopaedia of Mathematical Sciences: "... I think the volume is a great success and an excellent preparation for future volumes in the series. ... the introductory style of Egorov and Shubin is .. attractive. ... a welcome addition to the literature and I am looking forward to the appearance of more volumes of the Encyclopedia in the near future. ..." The Mathematical Intelligencer, 1993 "... According to the authors ... the work was written for nonspecialists and physicists but in my opinion almost every specialist will find something new ... in the text. The style is clear, the notations are chosen luckily. The most characteristic feature of the work is the accurate emphasis on the fundamental notions ..." Acta Scientiarum Mathematicarum, 1993 "... On the whole, a thorough overview on the classical aspects of the topic may be gained from that volume." Monatshefte für Mathematik, 1993 "... It is comparable in scope with the great Coura...
Collaboration in classical political economy and noncooperative game theory.
McCain, Roger A
2014-06-01
This commentary suggests (1) that there are precedents for Smaldino's "collaboration" in the history of economic thought before 1900 and (2) that the distinction of collaboration from what is thought of as cooperation in game theory is less clear than Smaldino suggests.
Quantum and classical theories of scattering of relativistic electrons in ultrathin crystals
Shulga, N F
2016-01-01
Quantum and classical theories are proposed of scattering of high energy electrons in ultrathin crystals. The quantum theory is based upon a special representation of the scattering amplitude in the form of the integral over the surface surrounding the crystal, and on the spectral method of determination of the wave function. The classical theory is based upon the solution of the equation of motion by numerical methods. The comparison is performed of quantum and classical differential cross-sections of scattering in the transitional range of crystal thicknesses, from those at which the channeling phenomenon is not developed up to those at which it is realized. It is shown that in this range of crystal thicknesses substantial difference of quantum and classical scattering cross-sections takes place for the electrons with the energy up to tens of MeV. With the energy increase such difference decreases but some quantum effects in scattering still remain.
Duran-Olivencia, Miguel A.; Yatsyshin, Peter; Lutsko, James F.; Kalliadasis, Serafim
2016-11-01
Classical density functional theory (DFT) for fluids and its dynamic extension (DDFT) provide an appealing mean-field framework for describing equilibrium and dynamics of complex soft matter systems. For a long time, homogeneous nucleation was considered to be outside the limits of applicability of DDFT. However, our recently developed mesoscopic nucleation theory (MeNT) based on fluctuating hydrodynamics, reconciles the inherent randomness of the nucleation process with the deterministic nature of DDFT. It turns out that in the weak-noise limit, the most likely path (MLP) for nucleation to occur is determined by the DDFT equations. We present computations of MLPs for homogeneous and heterogeneous nucleation in colloidal suspensions. For homogeneous nucleation, the MLP obtained is in excellent agreement with the reduced order-parameter description of MeNT, which predicts a multistage nucleation pathway. For heterogeneous nucleation, the presence of impurities in the fluid affects the MLP, but remarkably, the overall qualitative picture of homogeneous nucleation persists. Finally, we highlight the use of DDFT as a simulation tool, which is especially appealing as there are no known applications of MeNT to heterogeneous nucleation. We acknowledge financial support from the European Research Council via Advanced Grant No. 247031 and from EPSRC via Grants No. EP/L020564 and EP/L025159.
Kauffman Knot Invariant from SO(N) or Sp(N) Chern-Simons theory and the Potts Model
Astorino, Marco
2010-01-01
The expectation value of Wilson loop operators in three-dimensional SO(N) Chern-Simons gauge theory gives a known knot invariant: the Kauffman polynomial. Here this result is derived, at the first order, via a simple variational method. With the same procedure the skein relation for Sp(N) are also obtained. Jones polynomial arises as special cases: Sp(2), SO(-2) and SL(2,R). These results are confirmed and extended up to the second order, by means of perturbation theory, which moreover let us establish a duality relation between SO(+/-N) and Sp(-/+N) invariants. A correspondence between the firsts orders in perturbation theory of SO(-2), Sp(2) or SU(2) Chern-Simons quantum holonomies and the partition function of the Q=4 Potts Model is built.
Theory and Analysis of Classic Heavy Metal Harmony
Lilja, Esa
2009-01-01
This thesis explores melodic and harmonic features of heavy metal, and while doing so, explores various methods of music analysis; their applicability and limitations regarding the study of heavy metal music. The study is built on three general hypotheses according to which 1) acoustic characteristics play a significant role for chord constructing in heavy metal, 2) heavy metal has strong ties and similarities with other Western musical styles, and 3) theories and analytical methods of Wester...
Universality principle and the development of classical density functional theory
Institute of Scientific and Technical Information of China (English)
周世琦; 张晓琪
2002-01-01
The universality principle of the free energy density functional and the ‘test particle' trick by Percus are combined to construct the approximate free energy density functional or its functional derivative. Information about the bulk fluid ralial distribution function is integrated into the density functional approximation directly for the first time in the present methodology. The physical foundation of the present methodology also applies to the quantum density functional theory.
Derivation of the Special Theory of Relativity from Invariance of Action
Hushwater, V
2016-01-01
It is known that action is invariant in special relativity. The goal of this note is to show that the reverse statement is also correct, that special relativity follows from the postulate that action is invariant under the transformation from one inertial frame to another.
Classical light dispersion theory in a regular lattice
Marino, M.; Carati, A.; Galgani, L.
2007-04-01
We study the dynamics of an infinite regular lattice of classical charged oscillators. Each individual oscillator is described as a point particle subject to a harmonic restoring potential, to the retarded electromagnetic field generated by all the other particles, and to the radiation reaction expressed according to the Lorentz-Dirac equation. Exact normal mode solutions, describing the propagation of plane electromagnetic waves through the lattice, are obtained for the complete linearized system of infinitely many oscillators. At variance with all the available results, our method is valid for any values of the frequency, or of the ratio between wavelength and lattice parameter. A remarkable feature is that the proper inclusion of radiation reaction in the dynamics of the individual oscillators does not give rise to any extinction coefficient for the global normal modes of the lattice. The dispersion relations resulting from our solution are numerically studied for the case of a simple cubic lattice. New predictions are obtained in this way about the behavior of the crystal at frequencies near the proper oscillation frequency of the dipoles.
Opportunizing: A classic grounded theory study on business and management
Directory of Open Access Journals (Sweden)
Ólavur Christiansen
2006-11-01
Full Text Available Opportunizing emerged as the core variable of this classic GT study on business and management. Opportunizing is the recurrent main concern that businesses have to continually resolve, and it explains how companies recurrently create, identify, seize or exploit situations to maintain their growth or survival. Opportunizing is the recurrent creation and re-creation of opportunities in business. Opportunizing is basically what business managers do and do all the time. The problematic nature of opportunizing is resolved by a core social process ofopportunizing and its attached sub-processes that account for change over time and for the variations of the problematic nature of its resolution.Opportunizing has five main facets. These are conditional befriending (confidence building & modifying behavior,prospecting (e.g. information gaining, weighing up (information appraisal & decision-making, moment capturing (quick intervention for seizing strategic opportunities, andconfiguration matching (adjusting the business organization to abet the other activities of opportunizing.On a more abstract level, opportunizing has three more organizational facets: the physically boundary-less, the valuehierarchical, and the physically bounded. The first of these called perpetual opportunizing. This emerges from the conjunction of conditional befriending and prospecting. The second facet is called triggering opportunizing. It arises from the coming together of weighing up and moment capturing. The final facet is called spasmodic opportunizing. This happens when moment capturing and configuration matching unite.
Pressler, David E.
2012-03-01
A great discrepancy exists - the speed of light and the neutrino speed must be identical; as indicated by supernova1987A; yet, OPERA predicts faster-than-light neutrinos. Einstein's theories are based on the invariance of the speed of light, and no privileged Galilean frame of reference exists. Both of these hypotheses are in error and must be reconciled in order to solve the dilemma. The Michelson-Morley Experiment was misinterpreted - my Neoclassical Theory postulates that BOTH mirrors of the interferometer physically and absolutely move towards its center. The result is a three-directional-Contraction, (x, y, z axis), an actual distortion of space itself; a C-Space condition. ``PRESSLER'S LAW OF C-SPACE: The speed of light, c, will always be measured the same speed in all three directions (˜300,000 km/sec), in ones own inertial reference system, and will always be measured as having a different speed in all other inertial frames which are at a different kinetic energy level or at a location with a different strength gravity field'' Thus, the faster you go, motion, or the stronger the gravity field the smaller you get in all three directions. OPERA results are explained; at the surface of Earth, the strength of gravity field is at maximum -- below the earth's surface, time and space is less distorted; therefore, time is absolutely faster accordingly. Reference OPERA's preprint: Neutrino's faster time-effect due to altitude difference; (10-13ns) x c (299792458m) = 2.9 x 10-5 m/ns x distance (730085m) + 21.8m.) This is consistent with the OPERA result.
Finite-block-length analysis in classical and quantum information theory.
Hayashi, Masahito
2017-01-01
Coding technology is used in several information processing tasks. In particular, when noise during transmission disturbs communications, coding technology is employed to protect the information. However, there are two types of coding technology: coding in classical information theory and coding in quantum information theory. Although the physical media used to transmit information ultimately obey quantum mechanics, we need to choose the type of coding depending on the kind of information device, classical or quantum, that is being used. In both branches of information theory, there are many elegant theoretical results under the ideal assumption that an infinitely large system is available. In a realistic situation, we need to account for finite size effects. The present paper reviews finite size effects in classical and quantum information theory with respect to various topics, including applied aspects.
Gauge invariance properties and singularity cancellations in a modified PQCD
Cabo-Montes de Oca, Alejandro; Cabo, Alejandro; Rigol, Marcos
2006-01-01
The gauge-invariance properties and singularity elimination of the modified perturbation theory for QCD introduced in previous works, are investigated. The construction of the modified free propagators is generalized to include the dependence on the gauge parameter $\\alpha $. Further, a functional proof of the independence of the theory under the changes of the quantum and classical gauges is given. The singularities appearing in the perturbative expansion are eliminated by properly combining dimensional regularization with the Nakanishi infrared regularization for the invariant functions in the operator quantization of the $\\alpha$-dependent gauge theory. First-order evaluations of various quantities are presented, illustrating the gauge invariance-properties.
Momentum relation and classical limit in the future-not-included complex action theory
Nagao, Keiichi
2013-01-01
Studying the time development of the expectation value in the future-not-included complex action theory we point out that the momentum relation (relation analogous to $p=\\frac{\\partial L}{\\partial \\dot{q}}$), which was derived via Feynman path integral and was shown to be right in the future-included theory in our previous papers, is not valid in the future-not-included theory. We provide the correct momentum relation in the future-not-included theory, and argue that the future-not-included classical theory is described by a certain real action. In addition we provide another way to understand the time development of the future-not-included theory by utilizing the future-included theory. Furthermore, applying the method used in our previous paper to the future-not-included theory properly by introducing a formal Lagrangian, we derive the correct momentum relation in the future-not-included theory.
Momentum relation and classical limit in the future-not-included complex action theory
Nagao, Keiichi; Nielsen, Holger Bech
2013-07-01
Studying the time development of the expectation value in the future-not-included complex action theory, we point out that the momentum relation (the relation analogous to p=frac {partial L}{partial dot {q}}), which was derived via the Feynman path integral and was shown to be correct in the future-included theory in our previous papers, is not valid in the future-not-included theory. We provide the correct momentum relation in the future-not-included theory, and argue that the future-not-included classical theory is described by a certain real action. In addition, we provide another way to understand the time development of the future-not-included theory by utilizing the future-included theory. Furthermore, properly applying the method used in our previous paper to the future-not-included theory by introducing a formal Lagrangian, we derive the correct momentum relation in the future-not-included theory.
Solving effective field theory of interacting QCD pomerons in the semi-classical approximation
Bondarenko, S; Bondarenko, Sergey; Motyka, Leszek
2006-01-01
Effective field theory of BFKL pomerons interacting by QCD triple pomeron vertices is investigated. Classical equations of motion for the effective pomeron fields are presented being a minimal extension of the Balitsky-Kovchegov equation that incorporates both merging and splitting of the pomerons and that is self-dual. The equations are solved for symmetric boundary conditions. The solutions provide the dominant contribution to the scattering amplitudes in the semi-classical approximation. We find that for rapidities of the scattering larger than a critical value Y_c at least two classical solutions exist. Curiously, for each of the two classical solutions with the lowest action the symmetry between the projectile and the target is found to be spontaneously broken, being however preserved for the complete set of classical solutions. The solving configurations at rapidities Y>Y_c consist of a Gribov field being strongly suppressed even at very large gluon momenta and the complementary Gribov field that conver...
Quasi-classical theory of electronic flux density in electronically adiabatic molecular processes.
Diestler, D J
2012-11-26
The standard Born-Oppenheimer (BO) description of electronically adiabatic molecular processes predicts a vanishing electronic flux density (EFD). A previously proposed "coupled-channels" theory permits the extraction of the EFD from the BO wave function for one-electron diatomic systems, but attempts at generalization to many-electron polyatomic systems are frustrated by technical barriers. An alternative "quasi-classical" approach, which eliminates the explicit quantum dynamics of the electrons within a classical framework, yet retains the quantum character of the nuclear motion, appears capable of yielding EFDs for arbitrarily complex systems. Quasi-classical formulas for the EFD in simple systems agree with corresponding coupled-channels formulas. Results of the application of the new quasi-classical formula for the EFD to a model triatomic system indicate the potential of the quasi-classical scheme to elucidate the dynamical role of electrons in electronically adiabatic processes in more complex multiparticle systems.
A Four-Dimensional Continuum Theory of Space-Time and the Classical Physical Fields
Directory of Open Access Journals (Sweden)
Suhendro I.
2007-10-01
Full Text Available In this work, we attempt to describe the classical physical fields of gravity, electromagnetism, and the so-called intrinsic spin (chirality in terms of a set of fully geometrized constitutive equations. In our formalism, we treat the four-dimensional space-time continuum as a deformable medium and the classical fields as intrinsic stress and spin fields generated by infinitesimal displacements and rotations in the space-time continuum itself. In itself, the unifying continuum approach employed herein may suggest a possible unified field theory of the known classical physical fields.
Dressing the post-Newtonian two-body problem and classical effective field theory
Kol, Barak; Smolkin, Michael
2009-12-01
We apply a dressed perturbation theory to better organize and economize the computation of high orders of the 2-body effective action of an inspiralling post-Newtonian (PN) gravitating binary. We use the effective field theory approach with the nonrelativistic field decomposition (NRG fields). For that purpose we develop quite generally the dressing theory of a nonlinear classical field theory coupled to pointlike sources. We introduce dressed charges and propagators, but unlike the quantum theory there are no dressed bulk vertices. The dressed quantities are found to obey recursive integral equations which succinctly encode parts of the diagrammatic expansion, and are the classical version of the Schwinger-Dyson equations. Actually, the classical equations are somewhat stronger since they involve only finitely many quantities, unlike the quantum theory. Classical diagrams are shown to factorize exactly when they contain nonlinear worldline vertices, and we classify all the possible topologies of irreducible diagrams for low loop numbers. We apply the dressing program to our post-Newtonian case of interest. The dressed charges consist of the dressed energy-momentum tensor after a nonrelativistic decomposition, and we compute all dressed charges (in the harmonic gauge) appearing up to 2PN in the 2-body effective action (and more). We determine the irreducible skeleton diagrams up to 3PN and we employ the dressed charges to compute several terms beyond 2PN.
Werbos, P J
2003-01-01
Quantum Field Theory (QFT) makes predictions by combining two sets of assumptions: (1) quantum dynamics, such as a Schrodinger or Liouville equation; (2) quantum measurement, such as stochastic collapse to an eigenfunction of a measurement operator. A previous paper defined a classical density matrix R encoding the statistical moments of an ensemble of states of classical second-order Hamiltonian field theory. It proved Tr(RQ)=E(Q), etc., for the usual field operators as defined by Weinberg, and it proved that those observables of the classical system obey the usual Heisenberg dynamic equation. However, R itself obeys dynamics different from the usual Liouville equation! This paper derives those dynamics, and calculates the discrepancy between CFT and normal form QFT in predicting general observables g(Q,P). There is some preliminary evidence for the conjecture that the discrepancies disappear in equilibrium states (bound states and scattering states) for finite bosonic field theories. Even if not, they appea...
Development of a unified viscoplasticity constitutive model based on classical plasticity theory
Institute of Scientific and Technical Information of China (English)
GUAN Ping; LIU ChangChun; L(U) HeXiang
2009-01-01
The traditional unified viscoplasticity constitutive model can be only applied to metal materials. The study of the unified constitutive theory for metal materials has discovered the correlation between the classical plasticity theory and the unified viscoplasticity constitutive model, thus leading to the con-cepts of the classic plastic potential and yield surface in the unified constitutive model. Moreover, this research has given the continuous expression of the classical plastic multiplier and presented the corresponding constructive method, which extends its physical significance and lays down a good foundation for the application of the unified constitutive theory to the material analysis in more fields.This paper also introduces the unified constitutive model for metal materials and geo-materials. The numerical simulation indicates that the construction should be both reasonable and practical.
Development of a unified viscoplasticity constitutive model based on classical plasticity theory
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The traditional unified viscoplasticity constitutive model can be only applied to metal materials.The study of the unified constitutive theory for metal materials has discovered the correlation between the classical plasticity theory and the unified viscoplasticity constitutive model,thus leading to the con-cepts of the classic plastic potential and yield surface in the unified constitutive model.Moreover,this research has given the continuous expression of the classical plastic multiplier and presented the corresponding constructive method,which extends its physical significance and lays down a good foundation for the application of the unified constitutive theory to the material analysis in more fields.This paper also introduces the unified constitutive model for metal materials and geo-materials.The numerical simulation indicates that the construction should be both reasonable and practical.
Linking Rayleigh-Rice theory with near linear shift invariance in light scattering phenomena
Stover, John C.; Schroeder, Sven; Staats, Chris; Lopushenko, Vladimir; Church, Eugene
2016-09-01
Understanding topographic scatter has been the subject of many publications. For optically smooth surfaces that scatter only from roughness (and not from contamination, films or bulk defects) the Rayleigh-Rice relationship resulting from a rigorous electromagnetic treatment has been successfully used for over three decades and experimentally proven at wavelengths ranging from the X-Ray to the far infrared (even to radar waves). The "holy grail" of roughness-induced scatter would be a relationship that is not limited to just optically smooth surfaces, but could be used for any surface where the material optical constants and the surface power spectral density function (PSD) are known. Just input these quantities and calculate the BRDF associated with any source incident angle, wavelength and polarization. This is an extremely challenging problem, but that has not stopped a number of attempts. An intuitive requirement on such general relationships is that they must reduce to the simple Rayleigh-Rice formula for sufficiently smooth surfaces. Unfortunately that does not always happen. Because most optically smooth surfaces also scatter from non-topographic features, doubt creeps in about the accuracy of Rayleigh-Rice. This paper investigates these issues and explains some of the confusion generated in recent years. The authors believe there are measurement issues, scatter source issues and rough surface derivation issues, but that Rayleigh- Rice is accurate as formulated and should not be "corrected." Moreover, it will be shown that the empirically observed near shift invariance of surface scatter phenomena is a direct consequence of the Rayleigh-Rice theory.
Non-Abelian Geometric Phase, Floquet Theory, and Periodic Dynamical Invariants
Mostafazadeh, A
1998-01-01
For a periodic Hamiltonian, periodic dynamical invariants may be used to obtain non-degenerate cyclic states. This observation is generalized to the degenerate cyclic states, and the relation between the periodic dynamical invariants and the Floquet decompositions of the time-evolution operator is elucidated. In particular, a necessary condition for the occurrence of cyclic non-adiabatic non-Abelian geometrical phase is derived. Degenerate cyclic states are obtained for a magnetic dipole interacting with a precessing magnetic field.
Theory and computation of disturbance invariant sets for discrete-time linear systems
Directory of Open Access Journals (Sweden)
Kolmanovsky Ilya
1998-01-01
Full Text Available This paper considers the characterization and computation of invariant sets for discrete-time, time-invariant, linear systems with disturbance inputs whose values are confined to a specified compact set but are otherwise unknown. The emphasis is on determining maximal disturbance-invariant sets X that belong to a specified subset Γ of the state space. Such d-invariant sets have important applications in control problems where there are pointwise-in-time state constraints of the form χ ( t ∈ Γ . One purpose of the paper is to unite and extend in a rigorous way disparate results from the prior literature. In addition there are entirely new results. Specific contributions include: exploitation of the Pontryagin set difference to clarify conceptual matters and simplify mathematical developments, special properties of maximal invariant sets and conditions for their finite determination, algorithms for generating concrete representations of maximal invariant sets, practical computational questions, extension of the main results to general Lyapunov stable systems, applications of the computational techniques to the bounding of state and output response. Results on Lyapunov stable systems are applied to the implementation of a logic-based, nonlinear multimode regulator. For plants with disturbance inputs and state-control constraints it enlarges the constraint-admissible domain of attraction. Numerical examples illustrate the various theoretical and computational results.
Frank, Steven A.
2016-01-01
In nematodes, environmental or physiological perturbations alter death’s scaling of time. In human cancer, genetic perturbations alter death’s curvature of time. Those changes in scale and curvature follow the constraining contours of death’s invariant geometry. I show that the constraints arise from a fundamental extension to the theories of randomness, invariance and scale. A generalized Gompertz law follows. The constraints imposed by the invariant Gompertz geometry explain the tendency of perturbations to stretch or bend death’s scaling of time. Variability in death rate arises from a combination of constraining universal laws and particular biological processes.
Kapoyannis, A. S.; Kalkanis, G.
2017-03-01
We develop a simulation to facilitate the teaching of the photoelectric effect in an introductory course on quantum mechanics at undergraduate level. Through a Visual Basic program we describe the interaction of light with electrons in a metal conductor in the phenomenon according to the classical theory. The description includes both the microscopic interaction, as well as the predictions of the theory for the experimental results, arising from the microscopic scale. The predictions of the classical model are in stark contrast with the experimental results of a real photoelectric device.
Dye, H A
2011-01-01
We construct two knot invariants. The first knot invariant is a sum constructed using linking numbers. The second is an invariant of flat knots and is a formal sum of flat knots obtained by smoothing pairs of crossings. This invariant can be used in conjunction with other flat invariants, forming a family of invariants. Both invariants are constructed using the parity of a crossing.
Spontaneous Breaking of Scale Invariance in U(N) Chern-Simons Gauge Theories in Three Dimensions
Energy Technology Data Exchange (ETDEWEB)
Bardeen, William A. [Fermilab
2015-09-24
I explore the existence of a massive phase in a conformally invariant U(N) Chern-Simons gauge theories in D = 3 with matter fields in the fundamental representation. These models have attracted recent attention as being dual, in the conformal phase, to theories of higher spin gravity on AdS 4. Using the 0t Hooft large N expansion, exact solutions are obtained for scalar current correlators in the massive phase where the conformal symmetry is spontaneously broken. A massless dilaton appears as a composite state, and its properties are discussed. Solutions exist for matters field that are either bosons or fermions.
Spontaneous Breaking of Scale Invariance in U(N) Chern-Simons Gauge Theories in Three Dimensions
Energy Technology Data Exchange (ETDEWEB)
Bardeen, William [Fermilab
2014-10-24
I explore the existence of a massive phase in a conformally invariant U(N) Chern-Simons gauge theories in D = 3 with matter fields in the fundamental representation. These models have attracted recent attention as being dual, in the conformal phase, to theories of higher spin gravity on AdS 4. Using the 1t Hooft large N expansion, exact solutions are obtained for scalar current correlators in the massive phase where the conformal symmetry is spontaneously broken. A massless dilaton appears as a composite state, and its properties are discussed. Solutions exist for matters field that are either bosons or fermions.
Neo-classical theory of competition or Adam Smith's hand as mathematized ideology
McCauley, Joseph L.
2001-10-01
Orthodox economic theory (utility maximization, rational agents, efficient markets in equilibrium) is based on arbitrarily postulated, nonempiric notions. The disagreement between economic reality and a key feature of neo-classical economic theory was criticized empirically by Osborne. I show that the orthodox theory is internally self-inconsistent for the very reason suggested by Osborne: lack of invertibility of demand and supply as functions of price to obtain price as functions of supply and demand. The reason for the noninvertibililty arises from nonintegrable excess demand dynamics, a feature of their theory completely ignored by economists.
INVARIANT FORM AND INTEGRAL INVARIANTS ON K(A)HLER MANIFOLD
Institute of Scientific and Technical Information of China (English)
ZHANG Rong-ye
2006-01-01
The important notions and results of the integral invariants of Poincaré and lished first by E. Cartan in the classical mechanics are generalized to Hamilton mechanics on K(a)hler manifold, by the theory of modern geometry and advanced calculus, to get the corresponding wider and deeper results.
a Classical Isodual Theory of Antimatter and its Prediction of Antigravity
Santilli, Ruggero Maria
An inspection of the contemporary physics literature reveals that, while matter is treated at all levels of study, from Newtonian mechanics to quantum field theory, antimatter is solely treated at the level of second quantization. For the purpose of initiating the restoration of full equivalence in the treatment of matter and antimatter in due time, and as the classical foundations of an axiomatically consistent inclusion of gravitation in unified gauge theories recently appeared elsewhere, in this paper we present a classical representation of antimatter which begins at the primitive Newtonian level with corresponding formulations at all subsequent levels. By recalling that charge conjugation of particles into antiparticles is antiautomorphic, the proposed theory of antimatter is based on a new map, called isoduality, which is also antiautomorphic (and more generally, antiisomorphic), yet it is applicable beginning at the classical level and then persists at the quantum level where it becomes equivalent to charge conjugation. We therefore present, apparently for the first time, the classical isodual theory of antimatter, we identify the physical foundations of the theory as being the novel isodual Galilean, special and general relativities, and we show the compatibility of the theory with all available classical experimental data on antimatter. We identify the classical foundations of the prediction of antigravity for antimatter in the field of matter (or vice-versa) without any claim on its validity, and defer its resolution to specifically identified experiments. We identify the novel, classical, isodual electromagnetic waves which are predicted to be emitted by antimatter, the so-called space-time machine based on a novel non-Newtonian geometric propulsion, and other implications of the theory. We also introduce, apparently for the first time, the isodual space and time inversions and show that they are nontrivially different than the conventional ones, thus
Guillemin, Ernst A
2013-01-01
An eminent electrical engineer and authority on linear system theory presents this advanced treatise, which approaches the subject from the viewpoint of classical dynamics and covers Fourier methods. This volume will assist upper-level undergraduates and graduate students in moving from introductory courses toward an understanding of advanced network synthesis. 1963 edition.
Knot Invariants and M-Theory I: Hitchin Equations, Chern-Simons Actions, and the Surface Operators
Dasgupta, Keshav; Ramadevi, P; Tatar, Radu
2016-01-01
Recently Witten introduced a type IIB brane construction with certain boundary conditions to study knot invariants and Khovanov homology. The essential ingredients used in his work are the topologically twisted N = 4 Yang-Mills theory, localization equations and surface operators. In this paper we extend his construction in two possible ways. On one hand we show that a slight modification of Witten's brane construction could lead, using certain well defined duality transformations, to the model used by Ooguri-Vafa to study knot invariants using gravity duals. On the other hand, we argue that both these constructions, of Witten and of Ooguri-Vafa, lead to two different seven-dimensional manifolds in M-theory from where the topological theories may appear from certain twisting of the G-flux action. The non-abelian nature of the topological action may also be studied if we take the wrapped M2-brane states in the theory. We discuss explicit constructions of the seven-dimensional manifolds in M-theory, and show th...
Investigating the non-classical boundary conditions relevant to strain gradient theories
Jafari, Akbar; Ezzati, Meysam
2017-02-01
In the present study, two classes of non-classical constitutive equations consisting of the first and the second order strain gradients theories (FSG and SSG) were applied in order to develop the governing equations of static and free vibrational behavior of beam structures. The governing equations in orders of six and eight were constructed for FSG and SSG theories, respectively. Therefore, higher order or in other words non-classical boundary conditions (HOBCs or NCBCs) came into play in addition to the classical ones (CBCs). Some explanations were presented about the concept of the non-classical boundary conditions. Analytical and finite element (FE) approaches were employed to solve the governing equations. The analytical solutions were utilized in validation and convergence study of FE results. Comparisons were made with the relevant data reported in the open literature; however, to the best of the authors' knowledge, few references have been published on SSG theory and HOBCs. In the numerical studies, the effects of applying different combinations of CBCs and HOBCs to the static and free vibration behaviors of the beam were investigated. Moreover, the impacts of non-classical elastic constants and the beam size on its behavior were also studied.
Wang, Juven; Gu, Zheng-Cheng; Wen, Xiao-Gang
The challenge of identifying symmetry-protected topological states (SPTs) is due to their lack of symmetry-breaking order parameters and intrinsic topological orders. For this reason, it is impossible to formulate SPTs under Ginzburg-Landau theory or probe SPTs via fractionalized bulk excitations and topology-dependent ground state degeneracy. However, the partition functions from path integrals with various symmetry twists are universal SPT invariants, fully characterizing SPTs. In this work, we use gauge fields to represent those symmetry twists in closed spacetimes of any dimensionality and arbitrary topology. This allows us to express the SPT invariants in terms of continuum field theory. We show that SPT invariants of pure gauge actions describe the SPTs predicted by group cohomology, while the mixed gauge-gravity actions describe the beyond-group-cohomology SPTs, recently observed by Kapustin. We find new examples of mixed gauge-gravity actions for U(1) SPTs in 3+1D and 4+1D via the Stiefel-Whitney class and the gravitational Chern-Simons term. [Work based on Phys. Rev. Lett. 114, 031601 (2015) arXiv:1405.7689
Schlingman, Wayne M.; Prather, Edward E.; Wallace, Colin S.; Brissenden, Gina; Rudolph, Alexander L.
2012-01-01
This paper is the first in a series of investigations into the data from the recent national study using the Light and Spectroscopy Concept Inventory (LSCI). In this paper, we use classical test theory to form a framework of results that will be used to evaluate individual item difficulties, item discriminations, and the overall reliability of the…
A superfield generalization of the classical action-at-a-distance theory
Tugai, V. V.; Zheltukhin, A. A.
1994-07-01
A generalization of the Fokker-Schwarzschild- Tetrode-Wheeler-Feynman electromagnetic theory onto superspace is considered. The classical vector and spinor fields belonging to the Maxwell supermultiplet are built of the world-line coordinates of the charged particles in superspace.
Superfield generalization of the classical action-at-a-distance theory
Tugai, V. V.; Zheltukhin, A. A.
1995-04-01
A generalization of the Fokker-Schwarzschild-Tetrode-Wheeler-Feynman electromagnetic theory onto superspace is considered. The classical vector and spinor fields belonging to the Maxwell supermultiplet are built of the world-line coordinates of the charged particles in superspace.
Superfield generalization of the classical action-at-a-distance theory
Energy Technology Data Exchange (ETDEWEB)
Tugai, V.V. (Scientific Physicotechnological Center, 310145 Kharkov (Ukraine)); Zheltukhin, A.A. (Kharkov Physicotechnical Institute, 310108 Kharkov (Ukraine))
1995-04-15
A generalization of the Fokker-Schwarzschild-Tetrode-Wheeler-Feynman electromagnetic theory onto superspace is considered. The classical vector and spinor fields belonging to the Maxwell supermultiplet are built of the world-line coordinates of the charged particles in superspace.
Uniting the Spheres: Modern Feminist Theory and Classic Texts in AP English
Drew, Simao J. A.; Bosnic, Brenda G.
2008-01-01
High school teachers Simao J. A. Drew and Brenda G. Bosnic help familiarize students with gender role analysis and feminist theory. Students examine classic literature and contemporary texts, considering characters' historical, literary, and social contexts while expanding their understanding of how patterns of identity and gender norms exist and…
Wigner's dynamical transition state theory in phase space : classical and quantum
Waalkens, Holger; Schubert, Roman; Wiggins, Stephen
2008-01-01
We develop Wigner's approach to a dynamical transition state theory in phase space in both the classical and quantum mechanical settings. The key to our development is the construction of a normal form for describing the dynamics in the neighbourhood of a specific type of saddle point that governs t
Generalization of the Activated Complex Theory of Reaction Rates. II. Classical Mechanical Treatment
Marcus, R. A.
1964-01-01
In its usual classical form activated complex theory assumes a particular expression for the kinetic energy of the reacting system -- one associated with a rectilinear motion along the reaction coordinate. The derivation of the rate expression given in the present paper is based on the general kinetic energy expression.
Inflation and reheating in theories with spontaneous scale invariance symmetry breaking
Rinaldi, Massimiliano; Vanzo, Luciano
2016-07-01
We study a scale-invariant model of quadratic gravity with a nonminimally coupled scalar field. We focus on cosmological solutions and find that scale invariance is spontaneously broken and a mass scale naturally emerges. Before the symmetry breaking, the Universe undergoes an inflationary expansion with nearly the same observational predictions of Starobinsky's model. At the end of inflation, the Hubble parameter and the scalar field converge to a stable fixed point through damped oscillations and the usual Einstein-Hilbert action is recovered. The oscillations around the fixed point can reheat the Universe in various ways, and we study in detail some of these possibilities.
Lucas, Andrew; Schalm, Koenraad
2014-01-01
We compute the direct current resistivity of a scale-invariant, $d$-dimensional strange metal with dynamic critical exponent $z$ and hyperscaling-violating exponent $\\theta$, weakly perturbed by a scalar operator coupled to random-field disorder that locally breaks a $\\mathbb{Z}_2$ symmetry. Independent calculations via Einstein-Maxwell-Dilaton holography and memory matrix methods lead to the same results. We show that random field disorder has a strong effect on resistivity: charge carriers in the infrared are easily depleted, as the relaxation time for momentum is surprisingly small. In the course of our holographic calculation we introduce a non-trivial dilaton coupling to the disordered scalar, allowing us to study a strongly-coupled scale invariant theory with $\\theta \
Multipole Theory in Electromagnetism: Classical, Quantum and Symmetry Aspects, with Applications
Energy Technology Data Exchange (ETDEWEB)
Sihvola, Ari [Helsinki University of Technology (Finland)
2005-03-11
'Good reasons must, of force, give place to better', observes Brutus to Cassius, according to William Shakespeare in Julius Caesar. Roger Raab and Owen de Lange seem to agree, as they cite this sentence in the concluding chapter of their new book on the importance of exact multipole analysis in macroscopic electromagnetics. Very true and essential to remember in our daily research work. The two scientists from the University of Natal in Pietermaritzburg, South Africa (presently University of KwaZulu-Natal) have been working for a very long time on the accurate description of electric and magnetic response of matter and have published much of their findings in various physics journals. The present book gives us a clear and coherent exposition of many of these results. The important message of Raab and de Lange is that in the macroscopic description of matter, a correct balance between the various orders of electric and magnetic multipole terms has to be respected. If the inclusion of magnetic dipole terms is not complemented with electric quadrupoles, there is a risk of losing the translational invariance of certain important quantities. This means that the values of these quantities depend on the choice of the origin{exclamation_point} 'It can't be Nature, for it is not sense' is another of the apt literary citations in the book. Often monographs written by researchers look like they have been produced using a cut-and-paste technique; earlier published articles are included in the same book but, unfortunately, too little additional effort is expended into moulding the totality into a unified story. This is not the case with Raab and de Lange. The structure and the text flow of the book serve perfectly its important message. After the obligatory introduction of material response to electromagnetic fields, constitutive relations, basic quantum theory and spacetime properties, a chapter follows with transmission and scattering effects where
Sihvola, Ari
2005-03-01
`Good reasons must, of force, give place to better', observes Brutus to Cassius, according to William Shakespeare in Julius Caesar. Roger Raab and Owen de Lange seem to agree, as they cite this sentence in the concluding chapter of their new book on the importance of exact multipole analysis in macroscopic electromagnetics. Very true and essential to remember in our daily research work. The two scientists from the University of Natal in Pietermaritzburg, South Africa (presently University of KwaZulu-Natal) have been working for a very long time on the accurate description of electric and magnetic response of matter and have published much of their findings in various physics journals. The present book gives us a clear and coherent exposition of many of these results. The important message of Raab and de Lange is that in the macroscopic description of matter, a correct balance between the various orders of electric and magnetic multipole terms has to be respected. If the inclusion of magnetic dipole terms is not complemented with electric quadrupoles, there is a risk of losing the translational invariance of certain important quantities. This means that the values of these quantities depend on the choice of the origin! `It canÂ't be Nature, for it is not sense' is another of the apt literary citations in the book. Often monographs written by researchers look like they have been produced using a cut-and-paste technique; earlier published articles are included in the same book but, unfortunately, too little additional effort is expended into moulding the totality into a unified story. This is not the case with Raab and de Lange. The structure and the text flow of the book serve perfectly its important message. After the obligatory introduction of material response to electromagnetic fields, constitutive relations, basic quantum theory and spacetime properties, a chapter follows with transmission and scattering effects where everything seems to work well with the `old
Phonon interaction of electron in the translation-invariant strong-coupling theory
Lakhno, Victor D.
2015-01-01
A dependence of phonon interaction on the interelectronic distance is found for a translation-invariant (TI) strong-coupling bipolaron. It is shown that the charge induced by the electrons in a TI-bipolaron state is always greater than that in a bipolaron with spontaneously broken symmetry.
Are galaxy distributions scale invariant? A perspective from dynamical systems theory
McCauley, J L
1997-01-01
Unless there is evidence for fractal scaling with a single exponent over distances .1 <= r <= 100 h^-1 Mpc then the widely accepted notion of scale invariance of the correlation integral for .1 <= r <= 10 h^-1 Mpc must be questioned. The attempt to extract a scaling exponent \
Alg\\`ebres de Jordan et th\\'eorie des invariants
Blind, Bruno
2009-01-01
If V is a simple complex euclidean Jordan algebra and G the subgroup of GL(V) fixing the determinant of V, we give a unified description of the invariant algebras C[pV]^G, for p not greater than three.
The Postmodern Turn: Shall Classic Grounded Theory Take That Detour? A Review Essay
2006-01-01
Adherents to classic grounded theory have gotten used to spotting the pretenders working under the grounded theory banner. Some of these faux-GT researchers have worked in a fog, misunderstanding fundamentals of the method; these are the studies that leave us shaking our heads and wondering about the doctoral committee and peer reviewers who did not bother to find out more about the method they were evaluating. More infuriating are the authors who are claiming to improve on grounded theory, t...
Laine, M; Tassler, M
2007-01-01
Recently, a finite-temperature real-time static potential has been introduced via a Schr\\"odinger-type equation satisfied by a certain heavy quarkonium Green's function. Furthermore, it has been pointed out that it possesses an imaginary part, which induces a finite width for the tip of the quarkonium peak in the thermal dilepton production rate. The imaginary part originates from Landau-damping of low-frequency gauge fields, which are essentially classical due to their high occupation number. Here we show how the imaginary part can be measured with classical lattice gauge theory simulations, accounting non-perturbatively for the infrared sector of finite-temperature field theory. We demonstrate that a non-vanishing imaginary part indeed exists non-perturbatively; and that its value agrees semi-quantitatively with that predicted by Hard Loop resummed perturbation theory.
A New Conformal Theory of Semi-Classical Quantum General Relativity
Directory of Open Access Journals (Sweden)
Suhendro I.
2007-10-01
Full Text Available We consider a new four-dimensional formulation of semi-classical quantum general relativity in which the classical space-time manifold, whose intrinsic geometric properties give rise to the effects of gravitation, is allowed to evolve microscopically by means of a conformal function which is assumed to depend on some quantum mechanical wave function. As a result, the theory presented here produces a unified field theory of gravitation and (microscopic electromagnetism in a somewhat simple, effective manner. In the process, it is seen that electromagnetism is actually an emergent quantum field originating in some kind of stochastic smooth extension (evolution of the gravitational field in the general theory of relativity.
Effective model hierarchies for dynamic and static classical density functional theories
Energy Technology Data Exchange (ETDEWEB)
Majaniemi, S [Department of Applied Physics, Aalto University School of Science and Technology, PO Box 11100, FI-00076 Aalto (Finland); Provatas, N [Department of Materials Science and Engineering, McMaster University, 1280 Main Street West, Hamilton, ON, L8S-4L7 (Canada); Nonomura, M, E-mail: maj@fyslab.hut.f [Department of Physics, Graduate School of Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522 (Japan)
2010-09-15
The origin and methodology of deriving effective model hierarchies are presented with applications to solidification of crystalline solids. In particular, it is discussed how the form of the equations of motion and the effective parameters on larger scales can be obtained from the more microscopic models. It will be shown that tying together the dynamic structure of the projection operator formalism with static classical density functional theories can lead to incomplete (mass) transport properties even though the linearized hydrodynamics on large scales is correctly reproduced. To facilitate a more natural way of binding together the dynamics of the macrovariables and classical density functional theory, a dynamic generalization of density functional theory based on the nonequilibrium generating functional is suggested.
A nonlinear theory of tensor distributions
Vickers, J A
1998-01-01
The coordinate invariant theory of generalised functions of Colombeau and Meril is reviewed and extended to enable the construction of multi-index generalised tensor functions whose transformation laws coincide with their counterparts in classical distribution theory.
Studying thin film damping in a micro-beam resonator based on non-classical theories
Ghanbari, Mina; Hossainpour, Siamak; Rezazadeh, Ghader
2016-06-01
In this paper, a mathematical model is presented for studying thin film damping of the surrounding fluid in an in-plane oscillating micro-beam resonator. The proposed model for this study is made up of a clamped-clamped micro-beam bound between two fixed layers. The micro-gap between the micro-beam and fixed layers is filled with air. As classical theories are not properly capable of predicting the size dependence behaviors of the micro-beam, and also behavior of micro-scale fluid media, hence in the presented model, equation of motion governing longitudinal displacement of the micro-beam has been extracted based on non-local elasticity theory. Furthermore, the fluid field has been modeled based on micro-polar theory. These coupled equations have been simplified using Newton-Laplace and continuity equations. After transforming to non-dimensional form and linearizing, the equations have been discretized and solved simultaneously using a Galerkin-based reduced order model. Considering slip boundary conditions and applying a complex frequency approach, the equivalent damping ratio and quality factor of the micro-beam resonator have been obtained. The obtained values for the quality factor have been compared to those based on classical theories. We have shown that applying non-classical theories underestimate the values of the quality factor obtained based on classical theories. The effects of geometrical parameters of the micro-beam and micro-scale fluid field on the quality factor of the resonator have also been investigated.
Studying thin film damping in a micro-beam resonator based on non-classical theories
Institute of Scientific and Technical Information of China (English)
Mina Ghanbari; Siamak Hossainpour; Ghader Rezazadeh
2016-01-01
In this paper, a mathematical model is presented for studying thin film damping of the surrounding fluid in an in-plane oscillating micro-beam resonator. The proposed model for this study is made up of a clamped-clamped micro-beam bound between two fixed layers. The micro-gap between the micro-beam and fixed layers is filled with air. As classical theories are not properly capable of pre-dicting the size dependence behaviors of the micro-beam, and also behavior of micro-scale fluid media, hence in the presented model, equation of motion governing longitudinal displacement of the micro-beam has been extracted based on non-local elasticity theory. Furthermore, the fluid field has been modeled based on micro-polar theory. These coupled equations have been simplified using Newton-Laplace and continuity equations. After transforming to non-dimensional form and linearizing, the equations have been discretized and solved simultaneously using a Galerkin-based reduced order model. Considering slip boundary conditions and applying a complex frequency approach, the equivalent damping ratio and quality factor of the micro-beam resonator have been obtained. The obtained values for the quality factor have been compared to those based on classical theories. We have shown that applying non-classical theories underestimate the values of the quality factor obtained based on classical theo-ries. The effects of geometrical parameters of the micro-beam and micro-scale fluid field on the quality factor of the res-onator have also been investigated.
Zarei, Mohammad Hossein
2016-01-01
Although creating a unified theory in Elementary Particles Physics is still an open problem, there are a lot of attempts for unifying other fields of physics. Following such unifications, we regard a two dimensional (2D) classical $\\Phi^{4}$ field theory model to study several field theories with different symmetries in various dimensions. While the completeness of this model has been already proved by a mapping between statistical mechanics and quantum information theory, here, we take into account a fundamental systematic approach with purely mathematical basis to re-derive such completeness in a general manner. Due to simplicity and generality, we believe that our method leads to a general approach which can be understood by other physical communities as well as quantum information theorists. Furthermore, our proof of the completeness is not only a proof-of-principle, but also an interesting algorithmic proof. We consider a discrete version of a general field theory as an arbitrary polynomial function of f...
Sokolov, Igor V
2015-01-01
A theory of Symplectic Manifold with Contact Degeneracies (SMCD) was developed in [Zot'ev,2007]. The symplectic geometry uses an anti-symmetric tensor (closed differential form) such as a field tensor used in the classical field theory. The SMCD theory studies degeneracies of such form. In [Zot'ev,2011] the SMCD theory was applied to study a front of an electromagnetic pulsed field propagating into a region with no field. Here, the result of [Zot'ev,2011] is compared with the problem solution obtained using the well-known method presented in Witham, G.B., Linear and nonlinear waves, 1974. It is shown that the SMCD theory prediction is not supported by the result obtained with the Witham method.
Classical Weyl Transverse Gravity
Oda, Ichiro
2016-01-01
We study various classical aspects of the Weyl transverse (WTDiff) gravity in a general space-time dimension. First of all, we clarify a classical equivalence among three kinds of gravitational theories, those are, the conformally-invariant scalar tensor gravity, Einstein's general relativity and the WTDiff gravity via the gauge fixing procedure. Secondly, we show that in the WTDiff gravity the cosmological constant is a mere integration constant as in unimodular gravity, but it does not receive any radiative corrections unlike the unimodular gravity. A key point in this proof is to construct a covariantly conserved energy-momentum tensor, which is achieved on the basis of this equivalence relation. Thirdly, we demonstrate that the Noether current for the Weyl transformation is identically vanishing, thereby implying that the Weyl symmetry existing in both the conformally-invariant scalar tensor gravity and the WTDiff gravity is a "fake" symmetry. We find it possible to extend this proof to all matter fields,...
All-order bounds for correlation functions of gauge-invariant operators in Yang-Mills theory
Fröb, Markus B; Hollands, Stefan
2015-01-01
We give a complete, self-contained, and mathematically rigorous proof that Euclidean Yang-Mills theories are perturbatively renormalisable, in the sense that all correlation functions of arbitrary composite local operators fulfil suitable Ward identities. Our proof treats rigorously both all ultraviolet and infrared problems of the theory and provides, in the end, detailed analytical bounds on the correlation functions of an arbitrary number of composite local operators. These bounds are formulated in terms of certain weighted spanning trees extending between the insertion points of these operators. Our proofs are obtained within the framework of the Wilson-Wegner-Polchinski-Wetterich renormalisation group flow equations, combined with estimation techniques based on tree structures. Compared with previous mathematical treatments of massless theories without local gauge invariance [R. Guida and Ch. Kopper, arXiv:1103.5692; J. Holland, S. Hollands, and Ch. Kopper, arXiv:1411.1785] our constructions require seve...
Energy Technology Data Exchange (ETDEWEB)
Sahoo, Tapas; Pollak, Eli [Chemical Physics Department, Weizmann Institute of Science, 76100 Rehovot (Israel)
2015-08-14
A second order classical perturbation theory is developed to calculate the sticking probability of a particle scattered from an uncorrugated thermal surface. An analytic expression for the temperature dependent energy loss of the particle to the surface is derived by employing a one-dimensional generalized Langevin equation. The surface temperature reduces the energy loss, since the thermal surface transfers energy to the particle. Using a Gaussian energy loss kernel and the multiple collision theory of Fan and Manson [J. Chem. Phys. 130, 064703 (2009)], enables the determination of the fraction of particles trapped on the surface after subsequent momentum reversals of the colliding particle. This then leads to an estimate of the trapping probability. The theory is tested for the model scattering of Ar on a LiF(100) surface. Comparison with numerical simulations shows excellent agreement of the analytical theory with simulations, provided that the energy loss is determined by the second order perturbation theory.
Sahoo, Tapas; Pollak, Eli
2015-08-14
A second order classical perturbation theory is developed to calculate the sticking probability of a particle scattered from an uncorrugated thermal surface. An analytic expression for the temperature dependent energy loss of the particle to the surface is derived by employing a one-dimensional generalized Langevin equation. The surface temperature reduces the energy loss, since the thermal surface transfers energy to the particle. Using a Gaussian energy loss kernel and the multiple collision theory of Fan and Manson [J. Chem. Phys. 130, 064703 (2009)], enables the determination of the fraction of particles trapped on the surface after subsequent momentum reversals of the colliding particle. This then leads to an estimate of the trapping probability. The theory is tested for the model scattering of Ar on a LiF(100) surface. Comparison with numerical simulations shows excellent agreement of the analytical theory with simulations, provided that the energy loss is determined by the second order perturbation theory.
Cocycle Knot Invariants, Quandle Extensions, and Alexander Matrices
2002-01-01
The theory of quandle (co)homology and cocycle knot invariants is rapidly being developed. We begin with a summary of these recent advances. One such advance is the notion of a dynamical cocycle. We show how dynamical cocycles can be used to color knotted surfaces that are obtained from classical knots by twist-spinning. We also demonstrate relations between cocycle invariants and Alexander matrices.
Despina Hatzifotiadou: ALICE Master Class 1 - Theory: strange particles, V0 decays, invariant mass
CERN. Geneva
2016-01-01
This is the 1st of 4 short online videos. It contains an introduction to the first part of the exercise : what are strange particles, V0 decays, invariant mass. More details and related links on this indico event page. In more detail: What is Physics Master Classes Students after morning lectures, run programmes in the afternoon to do measurements. These tutorials are about how to use the software required to do these measurements. Background info and examples Looking for strange particles with ALICE http://aliceinfo.cern.ch/Public/MasterCL/MasterClassWebpage.html Introduction to first part of the exercise : what are strange particles, V0 decays, invariant mass. Demonstration of the software for the 1st part of the exercise - visual identification of V0s Introduction to second part of the exercise : strangeness enhancement; centrality of lead-lead collisions; explanation of efficiency, yield, background etc Demonstration of the software for the 2nd part of the exercise - invariant mass spec...
Pseudo-classical transport in a sheared magnetic field: Theory and simulation
Energy Technology Data Exchange (ETDEWEB)
Nevins, W.M.; Harte, J.; Gell, Y.
1979-11-01
The cross-field transport due to the trapping of electrons in a finite amplitude wave (pseudo-classical transport) is investigated. Both finite wave frequencies and magnetic shear are included. The single particle orbit equations are solved to obtain the trapping criterion as well as the trapped particle orbit width and bounce frequency. Using a random walk model, the scaling of the pseudo-classical transport coefficients with the parameters of the plasma and wave are deduced. This scaling is employed to extend a previous calculation of the transport coefficients to include magnetic shear which is found to reduce these transport coefficients. Computer simulations of this transport process are presented. The measured transport rates are in very good agreement with the previous kinetic calculation in the absence of magnetic shear and with this extension of pseudo-classical transport theory which includes magnetic shear.
Classical diffusion and quantum level velocities: systematic deviations from random matrix theory.
Lakshminarayan, A; Cerruti, N R; Tomsovic, S
1999-10-01
We study the response of the quasienergy levels in the context of quantized chaotic systems through the level velocity variance and relate them to classical diffusion coefficients using detailed semiclassical analysis. The systematic deviations from random matrix theory, assuming independence of eigenvectors from eigenvalues, are shown to be connected to classical higher-order time correlations of the chaotic system. We study the standard map as a specific example, and thus the well-known oscillatory behavior of the diffusion coefficient with respect to the parameter is reflected exactly in the oscillations of the variance of the level velocities. We study the case of mixed phase-space dynamics as well and note a transition in the scaling properties of the variance that occurs along with the classical transition to chaos.
Cohen, D; Kottos, T
2001-03-01
We study a classically chaotic system that is described by a Hamiltonian H(Q,P;x), where (Q,P) are the canonical coordinates of a particle in a two-dimensional well, and x is a parameter. By changing x we can deform the "shape" of the well. The quantum eigenstates of the system are /n(x)>. We analyze numerically how the parametric kernel P(n/m)=//(2) evolves as a function of delta(x)[triple bond](x-x(0)). This kernel, regarded as a function of n-m, characterizes the shape of the wave functions, and it also can be interpreted as the local density of states. The kernel P(n/m) has a well-defined classical limit, and the study addresses the issue of quantum-classical correspondence. Both the perturbative and the nonperturbative regimes are explored. The limitations of the random matrix theory approach are demonstrated.
Khrennikov, Andrei
2017-02-01
The scientific methodology based on two descriptive levels, ontic (reality as it is) and epistemic (observational), is briefly presented. Following Schrödinger, we point to the possible gap between these two descriptions. Our main aim is to show that, although ontic entities may be unaccessible for observations, they can be useful for clarification of the physical nature of operational epistemic entities. We illustrate this thesis by the concrete example: starting with the concrete ontic model preceding quantum mechanics (the latter is treated as an epistemic model), namely, prequantum classical statistical field theory (PCSFT), we propose the natural physical interpretation for the basic quantum mechanical entity-the quantum state ("wave function"). The correspondence PCSFT ↦ QM is not straightforward, it couples the covariance operators of classical (prequantum) random fields with the quantum density operators. We use this correspondence to clarify the physical meaning of the pure quantum state and the superposition principle-by using the formalism of classical field correlations.
Classical R-matrix theory of dispersionless systems: I. (1+1)-dimension theory
Energy Technology Data Exchange (ETDEWEB)
Blaszak, Maciej; Szablikowski, Blazej M [Institute of Physics, A Mickiewicz University, Umultowska 85, 61-614 Poznan (Poland)
2002-12-06
A systematic way of construction of (1+1)-dimensional dispersionless integrable Hamiltonian systems is presented. The method is based on the classical R-matrix on Poisson algebras of formal Laurent series. Results are illustrated with the known and new (1+1)-dimensional dispersionless systems.
Classical R-matrix theory of dispersionless systems: II. (2+1) dimension theory
Energy Technology Data Exchange (ETDEWEB)
Blaszak, Maciej; Szablikowski, Blazej M [Institute of Physics, A Mickiewicz University, Umultowska 85, 61-614 Poznan (Poland)
2002-12-06
A systematic way of constructing (2+1)-dimensional dispersionless integrable Hamiltonian systems is presented. The method is based on the so-called central extension procedure and classical R-matrix applied to the Poisson algebras of formal Laurent series. Results are illustrated with the known and new (2+1)-dimensional dispersionless systems.
Heavy Quark Thermalization in Classical Lattice Gauge Theory Lessons for Strongly-Coupled QCD
Laine, Mikko; Philipsen, Owe; Tassler, Marcus
2009-01-01
Thermalization of a heavy quark near rest is controlled by the correlator of two electric fields along a temporal Wilson line. We address this correlator within real-time, classical lattice Yang-Mills theory, and elaborate on the analogies that exist with the dynamics of hot QCD. In the weak-coupling limit, it can be shown analytically that the dynamics on the two sides are closely related to each other. For intermediate couplings, we carry out non-perturbative simulations within the classical theory, showing that the leading term in the weak-coupling expansion significantly underestimates the heavy quark thermalization rate. Our analytic and numerical results also yield a general understanding concerning the overall shape of the spectral function corresponding to the electric field correlator, which may be helpful in subsequent efforts to reconstruct it from Euclidean lattice Monte Carlo simulations.
Extended hydrodynamic approach to quantum-classical nonequilibrium evolution. I. Theory.
Bousquet, David; Hughes, Keith H; Micha, David A; Burghardt, Irene
2011-02-14
A mixed quantum-classical formulation is developed for a quantum subsystem in strong interaction with an N-particle environment, to be treated as classical in the framework of a hydrodynamic representation. Starting from the quantum Liouville equation for the N-particle distribution and the corresponding reduced single-particle distribution, exact quantum hydrodynamic equations are obtained for the momentum moments of the single-particle distribution coupled to a discretized quantum subsystem. The quantum-classical limit is subsequently taken and the resulting hierarchy of equations is further approximated by various closure schemes. These include, in particular, (i) a Grad-Hermite-type closure, (ii) a Gaussian closure at the level of a quantum-classical local Maxwellian distribution, and (iii) a dynamical density functional theory approximation by which the hydrodynamic pressure term is replaced by a free energy functional derivative. The latter limit yields a mixed quantum-classical formulation which has previously been introduced by I. Burghardt and B. Bagchi, Chem. Phys. 134, 343 (2006).
Brst Cohomology and Invariants of 4D Gravity in Ashtekar Variables
Chang, L N; Chang, Lay Nam; Soo, Chopin
1992-01-01
We discuss the BRST cohomologies of the invariants associated with the description of classical and quantum gravity in four dimensions, using the Ashtekar variables. These invariants are constructed from several BRST cohomology sequences. They provide a systematic and clear characterization of non-local observables in general relativity with unbroken diffeomorphism invariance, and could yield further differential invariants for four-manifolds. The theory includes fluctuations of the vierbein fields, but there exits a non-trivial phase which can be expressed in terms of Witten's topological quantum field theory. In this phase, the descent sequences are degenerate, and the corresponding classical solutions can be identified with the conformally self-dual sector of Einstein manifolds. The full theory includes fluctuations which bring the system out of this sector while preserving diffeomorphism invariance.
Classical field theories of first order and lagrangian submanifolds of premultisymplectic manifolds
Campos, Cédric M; Marrero, Juan Carlos
2011-01-01
A description of classical field theories of first order in terms of Lagrangian submanifolds of premultisymplectic manifolds is presented. For this purpose, a Tulczyjew's triple associated with a fibration is discussed. The triple is adapted to the extended Hamiltonian formalism. Using this triple, we prove that Euler-Lagrange and Hamilton-De Donder-Weyl equations are the local equations defining Lagrangian submanifolds of a premultisymplectic manifold.
Relativistic semi-classical theory of atom ionization in ultra-intense laser
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
A relativistic semi-classical theory (RSCT) of H-atom ionizationin ultra-intense laser (UIL) is proposed. A relativistic analytical expression for ionization probability of H-atom in its ground state is given. This expression, compared with non-relativistic expression, clearly shows the effects of the magnet vector in the laser, the non-dipole approximation and the relativistic mass-energy relation on the ionization processes. At the same time, we show that under some conditions the relativistic expression reduces to the non-relativistic expression of non-dipole approximation. At last, some possible applications of the relativistic theory are briefly stated.
Charged free fermions, vertex operators and the classical theory of conjugate nets
Energy Technology Data Exchange (ETDEWEB)
Doliwa, Adam [Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Rome (Italy); Instytut Fizyki Teoretycznej, Uniwersytet Warszawski, Warsaw (Poland); Manas, Manuel [Departamento de Matematica Aplicada y Estadistica, EUIT Aeronautica, Universidad Politecnica de Madrid, Madrid (Spain); Departamento de Fisica Teorica, Universidad Complutense, Madrid (Spain); Martinez Alonso, Luis; Medina, Elena [Departamento de Matematicas, Universidad de Cadiz, Cadiz (Spain); Santini, Paolo Maria [Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Rome (Italy); Dipartimento di Fisica, Universita di Catania, Catania (Italy)
1999-02-19
We show that the quantum field theoretical formulation of the {tau}-function theory has a geometrical interpretation within the classical transformation theory of conjugate nets. In particular, we prove that (i) the partial charge transformations preserving the neutral sector are Laplace transformations, (ii) the basic vertex operators are Levy and adjoint Levy transformations and (iii) the diagonal soliton vertex operators generate fundamental transformations. We also show that the bilinear identity for the multicomponent Kadomtsev-Petviashvili hierarchy becomes, through a generalized Miwa map, a bilinear identity for the multidimensional quadrilateral lattice equations. (author)
Kelton, K. F.; Falster, R.; Gambaro, D.; Olmo, M.; Cornara, M.; Wei, P. F.
1999-06-01
Quantitative measurements of the oxygen precipitate rate as a function of annealing were made in Czochralski-grown silicon wafers that contained different initial concentrations of oxygen. All wafers were annealed at 1000 °C for 15 min to ensure that the initial cluster-size distributions were identical in all samples of the same composition prior to the multi-step annealing treatments used for the precipitation studies. The experimental data are compared with numerical predictions for time-dependent nucleation within the classical theory of nucleation. Quantitative agreement is obtained between the measured and calculated densities of oxygen precipitates for nucleation temperatures greater than 600 °C, but only over a narrow range of oxygen composition. Below 600 °C, the measured density for all samples is orders of magnitude larger than is predicted from the model. Further, the measured data show an anomalously small temperature dependence for the induction time for nucleation that does not scale with the diffusion coefficient, as expected from the classical theory of nucleation. Fundamentally, the classical theory of nucleation cannot explain the time-dependent nucleation of oxygen precipitates for temperatures below 650 °C. A possible reason is given.
A scale invariance criterion for LES parametrizations
Directory of Open Access Journals (Sweden)
Urs Schaefer-Rolffs
2015-01-01
Full Text Available Turbulent kinetic energy cascades in fluid dynamical systems are usually characterized by scale invariance. However, representations of subgrid scales in large eddy simulations do not necessarily fulfill this constraint. So far, scale invariance has been considered in the context of isotropic, incompressible, and three-dimensional turbulence. In the present paper, the theory is extended to compressible flows that obey the hydrostatic approximation, as well as to corresponding subgrid-scale parametrizations. A criterion is presented to check if the symmetries of the governing equations are correctly translated into the equations used in numerical models. By applying scaling transformations to the model equations, relations between the scaling factors are obtained by demanding that the mathematical structure of the equations does not change.The criterion is validated by recovering the breakdown of scale invariance in the classical Smagorinsky model and confirming scale invariance for the Dynamic Smagorinsky Model. The criterion also shows that the compressible continuity equation is intrinsically scale-invariant. The criterion also proves that a scale-invariant turbulent kinetic energy equation or a scale-invariant equation of motion for a passive tracer is obtained only with a dynamic mixing length. For large-scale atmospheric flows governed by the hydrostatic balance the energy cascade is due to horizontal advection and the vertical length scale exhibits a scaling behaviour that is different from that derived for horizontal length scales.
Energy Technology Data Exchange (ETDEWEB)
Christe, P.; Flume, R.
1987-04-09
We investigate the structure of the linear differential operators whose solutions determine the four-point correlations of primary operators in the d=2 conformally invariant SU(2) sigma-model with Wess-Zumino term and the d=2 critical statistical systems with central Virasoro charge smaller than one. Factorisation properties of the differential operators are related to a finite closure of the operator algebras. We recover the selection and fusion rules of Fateev, Zamolodchikov and Gepner, Witten for the SU(2) sigma-model. It is outlined how the results of the SU(2) model can be used for the identification of closed operator algebras in the statistical model.
Energy Technology Data Exchange (ETDEWEB)
Christe, P.; Flume, R.
1986-10-01
We investigate the structure of the linear differential operators whose solutions determine the four point correlations of primary operators in the d=2 conformally invariant SU(2) sigma-model with Wess-Zumino term and the d=2 critical statistical systems with central Virasoro charge smaller than one. Factorisation properties of the differential operators are related to a finite closure of the operator algebras. We recover the selection and fusion rules of Fateev, Zamolodchikov and Gepner, Witten for the SU(2) sigma-model. It is outlined how the results of the SU(2) model can be used for the identification of closed operator algebras in the statistical model.
A theory of solving TAP equations for Ising models with general invariant random matrices
DEFF Research Database (Denmark)
Opper, Manfred; Çakmak, Burak; Winther, Ole
2016-01-01
We consider the problem of solving TAP mean field equations by iteration for Ising models with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical functional approach that in the thermodynamic limit yields a...... the iteration dependent on a Gaussian distributed field only. The TAP magnetizations are stable fixed points if a de Almeida–Thouless stability criterion is fulfilled. We illustrate our method explicitly for coupling matrices drawn from the random orthogonal ensemble....
A High Order Theory for Linear Thermoelastic Shells: Comparison with Classical Theories
Directory of Open Access Journals (Sweden)
V. V. Zozulya
2013-01-01
Full Text Available A high order theory for linear thermoelasticity and heat conductivity of shells has been developed. The proposed theory is based on expansion of the 3-D equations of theory of thermoelasticity and heat conductivity into Fourier series in terms of Legendre polynomials. The first physical quantities that describe thermodynamic state have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate. Thereby all equations of elasticity and heat conductivity including generalized Hooke's and Fourier's laws have been transformed to the corresponding equations for coefficients of the polynomial expansion. Then in the same way as in the 3D theories system of differential equations in terms of displacements and boundary conditions for Fourier coefficients has been obtained. First approximation theory is considered in more detail. The obtained equations for the first approximation theory are compared with the corresponding equations for Timoshenko's and Kirchhoff-Love's theories. Special case of plates and cylindrical shell is also considered, and corresponding equations in displacements are presented.
Chaos, scaling and existence of a continuum limit in classical non-Abelian lattice gauge theory
Energy Technology Data Exchange (ETDEWEB)
Nielsen, H.B. [Niels Bohr Inst., Kobenhavn (Denmark); Rugh, H.H. [Univ. of Warwick, Coventry (United Kingdom); Rugh, S.E. [Los Alamos National Lab., NM (United States)
1996-12-31
We discuss space-time chaos and scaling properties for classical non-Abelian gauge fields discretized on a spatial lattice. We emphasize that there is a {open_quote}no go{close_quotes} for simulating the original continuum classical gauge fields over a long time span since there is a never ending dynamical cascading towards the ultraviolet. We note that the temporal chaotic properties of the original continuum gauge fields and the lattice gauge system have entirely different scaling properties thereby emphasizing that they are entirely different dynamical systems which have only very little in common. Considered as a statistical system in its own right the lattice gauge system in a situation where it has reached equilibrium comes closest to what could be termed a {open_quotes}continuum limit{close_quotes} in the limit of very small energies (weak non-linearities). We discuss the lattice system both in the limit for small energies and in the limit of high energies where we show that there is a saturation of the temporal chaos as a pure lattice artifact. Our discussion focuses not only on the temporal correlations but to a large extent also on the spatial correlations in the lattice system. We argue that various conclusions of physics have been based on monitoring the non-Abelian lattice system in regimes where the fields are correlated over few lattice units only. This is further evidenced by comparison with results for Abelian lattice gauge theory. How the real time simulations of the classical lattice gauge theory may reach contact with the real time evolution of (semi-classical aspects of) the quantum gauge theory (e.g. Q.C.D.) is left an important question to be further examined.
Cubic surfaces and their invariants: Some memories of Raymond Stora
Directory of Open Access Journals (Sweden)
Michel Bauer
2016-11-01
I then turn to the study of the family of cubic surfaces. They depend on 20 parameters, and the action of the 15 parameter group SL4(C splits the family in orbits depending on 5 parameters. This takes us into the realm of (geometric invariant theory. I review briefly the classical theorems on the structure of the ring of polynomial invariants and illustrate its many facets by looking at a simple example, before turning to the already involved case of cubic surfaces. The invariant ring was described in the 19th century. I show how to retrieve this description via counting/generating functions and character formulae.
Is That a Real Theory or Did You Just Make It Up? Teaching Classic Grounded Theory
Directory of Open Access Journals (Sweden)
Odis E. Simmons, Ph.D.
2010-06-01
Full Text Available The title of this paper was derived from an incident I observed some years ago while accompanying a highly talented musician-songwriter friend to a performance. During a break, an audience member approached him to compliment the last song he had performed. He had written both the music and the lyrics to the song, one of many he had written. The audience member queried, “Is that a real song, or did you just make it up?” A touch amused, and not knowing whether he should be flattered or insulted, he politely replied, “It is a real song and I made it up.”This episode puts in mind a similar attitude in the social sciences that Glaser and Strauss (1967 noted, in which a small number of ’theoretical capitalists’ originate what are considered to be “real” theories and others are relegated to the role of “proletariat” testers. The means by which these theorists derived their theories remained largely mysterious. Unleashing proletariat testers was one of the chief rationales behind Glaser and Strauss’ development of grounded theory. It brought a democratic option into the social sciences that enabled anyone who learned the methodology to generate theory. The democratic ethos of the methodology may also have inadvertently unleashed an abundance of aspiring remodelers of the methodology, who unfortunately have eroded its primary purpose—to generate theories that are fully grounded in data rather than speculation or ideology.
Force-Field Functor Theory: Classical Force-Fields which Reproduce Equilibrium Quantum Distributions
Directory of Open Access Journals (Sweden)
Ryan eBabbush
2013-10-01
Full Text Available Feynman and Hibbs were the first to variationally determine an effective potential whose associated classical canonical ensemble approximates the exact quantum partition function. We examine the existence of a map between the local potential and an effective classical potential which matches the exact quantum equilibrium density and partition function. The usefulness of such a mapping rests in its ability to readily improve Born-Oppenheimer potentials for use with classical sampling. We show that such a map is unique and must exist. To explore the feasibility of using this result to improve classical molecular mechanics, we numerically produce a map from a library of randomly generated one-dimensional potential/effective potential pairs then evaluate its performance on independent test problems. We also apply the map to simulate liquid para-hydrogen, finding that the resulting radial pair distribution functions agree well with path integral Monte Carlo simulations. The surprising accessibility and transferability of the technique suggest a quantitative route to adapting Born-Oppenheimer potentials, with a motivation similar in spirit to the powerful ideas and approximations of density functional theory.
Camilleri, Kristian; Schlosshauer, Maximilian
2015-02-01
Niels Bohr's doctrine of the primacy of "classical concepts" is arguably his most criticized and misunderstood view. We present a new, careful historical analysis that makes clear that Bohr's doctrine was primarily an epistemological thesis, derived from his understanding of the functional role of experiment. A hitherto largely overlooked disagreement between Bohr and Heisenberg about the movability of the "cut" between measuring apparatus and observed quantum system supports the view that, for Bohr, such a cut did not originate in dynamical (ontological) considerations, but rather in functional (epistemological) considerations. As such, both the motivation and the target of Bohr's doctrine of classical concepts are of a fundamentally different nature than what is understood as the dynamical problem of the quantum-to-classical transition. Our analysis suggests that, contrary to claims often found in the literature, Bohr's doctrine is not, and cannot be, at odds with proposed solutions to the dynamical problem of the quantum-classical transition that were pursued by several of Bohr's followers and culminated in the development of decoherence theory.
Babbush, Ryan; Parkhill, John; Aspuru-Guzik, Alán
2013-01-01
Feynman and Hibbs were the first to variationally determine an effective potential whose associated classical canonical ensemble approximates the exact quantum partition function. We examine the existence of a map between the local potential and an effective classical potential which matches the exact quantum equilibrium density and partition function. The usefulness of such a mapping rests in its ability to readily improve Born-Oppenheimer potentials for use with classical sampling. We show that such a map is unique and must exist. To explore the feasibility of using this result to improve classical molecular mechanics, we numerically produce a map from a library of randomly generated one-dimensional potential/effective potential pairs then evaluate its performance on independent test problems. We also apply the map to simulate liquid para-hydrogen, finding that the resulting radial pair distribution functions agree well with path integral Monte Carlo simulations. The surprising accessibility and transferability of the technique suggest a quantitative route to adapting Born-Oppenheimer potentials, with a motivation similar in spirit to the powerful ideas and approximations of density functional theory.
Borisenko, Alexander
2016-05-01
During the processes of nucleation and growth of a precipitate cluster from a supersaturated solution, the diffusion flux between the cluster and the solution changes the solute concentration near the cluster-solution interface from its average bulk value. This feature affects the rates of attachment and detachment of solute atoms at the interface, and, therefore, the entire nucleation-growth kinetics is altered. Unless quite obvious, this effect has been ignored in classical nucleation theory. To illustrate the results of this approach, for the case of homogeneous nucleation, we calculate the total solubility and the nucleation rate as functions of two parameters of the model (the reduced interface energy and the inverse second Damköhler number), and we compare these results to the classical ones. One can conclude that discrepancies with classical nucleation theory are great in the diffusion-limited regime, when the rate of bulk diffusion is small compared to the rate of interface reactions, while in the opposite interface-limited case they vanish.
The quench map in an integrable classical field theory: nonlinear Schrödinger equation
Caudrelier, Vincent; Doyon, Benjamin
2016-11-01
We study the non-equilibrium dynamics obtained by an abrupt change (a quench) in the parameters of an integrable classical field theory, the nonlinear Schrödinger equation. We first consider explicit one-soliton examples, which we fully describe by solving the direct part of the inverse scattering problem. We then develop some aspects of the general theory using elements of the inverse scattering method. For this purpose, we introduce the quench map which acts on the space of scattering data and represents the change of parameter with fixed field configuration (initial condition). We describe some of its analytic properties by implementing a higher level version of the inverse scattering method, and we discuss the applications of Darboux–Bäcklund transformations, Gelfand–Levitan–Marchenko equations and the Rosales series solution to a related, dual quench problem. Finally, we comment on the interplay between quantum and classical tools around the theme of quenches and on the usefulness of the quantization of our classical approach to the quantum quench problem.
[A non-classical approach to medical practices: Michel Foucault and Actor-Network Theory].
Bińczyk, E
2001-01-01
The text presents an analysis of medical practices stemming from two sources: Michel Foucault's conception and the research of Annemarie Mol and John Law, representatives of a trend known as Actor-Network Theory. Both approaches reveal significant theoretical kinship: they can be successfully consigned to the framework of non-classical sociology of science. I initially refer to the cited conceptions as a version of non-classical sociology of medicine. The identity of non-classical sociology of medicine hinges on the fact that it undermines the possibility of objective definitions of disease, health and body. These are rather approached as variable social and historical phenomena, co-constituted by medical practices. To both Foucault and Mol the main object of interest was not medicine as such, but rather the network of medical practices. Mol and Law sketch a new theoretical perspective for the analysis of medical practices. They attempt to go beyond the dichotomous scheme of thinking about the human body as an object of medical research and the subject of private experience. Research on patients suffering blood-sugar deficiency provide the empirical background for the thesis of Actor-Network Theory representatives. Michel Foucault's conceptions are extremely critical of medical practices. The French researcher describes the processes of 'medicalising' Western society as the emergence of a new type of power. He attempts to sensitise the reader to the ethical dimension of the processes of medicalising society.
Motion in classical field theories and the foundations of the self-force problem
Harte, Abraham I
2014-01-01
This article serves as a pedagogical introduction to the problem of motion in classical field theories. The primary focus is on self-interaction: How does an object's own field affect its motion? General laws governing the self-force and self-torque are derived using simple, non-perturbative arguments. The relevant concepts are developed gradually by considering motion in a series of increasingly complicated theories. Newtonian gravity is discussed first, then Klein-Gordon theory, electromagnetism, and finally general relativity. Linear and angular momenta as well as centers of mass are defined in each of these cases. Multipole expansions for the force and torque are then derived to all orders for arbitrarily self-interacting extended objects. These expansions are found to be structurally identical to the laws of motion satisfied by extended test bodies, except that all relevant fields are replaced by effective versions which exclude the self-fields in a particular sense. Regularization methods traditionally ...
Charge transport in high mobility molecular semiconductors: classical models and new theories.
Troisi, Alessandro
2011-05-01
The theories developed since the fifties to describe charge transport in molecular crystals proved to be inadequate for the most promising classes of high mobility molecular semiconductors identified in the recent years, including for example pentacene and rubrene. After reviewing at an elementary level the classical theories, which still provide the language for the understanding of charge transport in these systems, this tutorial review outlines the recent experimental and computational evidence that prompted the development of new theories of charge transport in molecular crystals. A critical discussion will illustrate how very rarely it is possible to assume a charge hopping mechanism for high mobility organic crystals at any temperature. Recent models based on the effect of non-local electron-phonon coupling, dynamic disorder, coexistence of localized and delocalized states are reviewed. Additionally, a few more recent avenues of theoretical investigation, including the study of defect states, are discussed.
Kim, Seulong
2016-01-01
Bi-isotropic media, which include isotropic chiral media and Tellegen media as special cases, are the most general form of linear isotropic media where the electric displacement and the magnetic induction are related to both the electric field and the magnetic intensity. In inhomogeneous bi-isotropic media, electromagnetic waves of two different polarizations are coupled to each other. In this paper, we develop a generalized version of the invariant imbedding method for the study of wave propagation in arbitrarily-inhomogeneous stratified bi-isotropic media, which can be used to solve the coupled wave propagation problem accurately and efficiently. We verify the validity and usefulness of the method by applying it to several examples, including the wave propagation in a uniform chiral slab, the surface wave excitation in a bilayer system made of a layer of Tellegen medium and a metal layer, and the mode conversion of transverse electromagnetic waves into longitudinal plasma oscillations in inhomogeneous Telle...
Wagler, Amy; Wagler, Ron
2013-01-01
The Measure of Acceptance of the Theory of Evolution (MATE) was constructed to be a single-factor instrument that assesses an individual's overall acceptance of evolutionary theory. The MATE was validated and the scores resulting from the MATE were found to be reliable for the population of inservice high school biology teachers. However,…
Oancea, Alexandru
2011-01-01
This is an overview of some of the invariants that were discovered by Welschinger in the context of enumerative real algebraic geometry. Their definition finds a natural setup in real symplectic geometry. In particular, they can be studied using techniques from symplectic field theory, of which we also give a sample. Welschinger invariants are real analogues of certain Gromov-Witten invariants. This article is an extended set of notes for a talk at the Bourbaki seminar in April 2011.
The principle of stationary nonconservative action for classical mechanics and field theories
Galley, Chad R; Stein, Leo C
2014-01-01
We further develop a recently introduced variational principle of stationary action for problems in nonconservative classical mechanics and extend it to classical field theories. The variational calculus used is consistent with an initial value formulation of physical problems and allows for time-irreversible processes, such as dissipation, to be included at the level of the action. In this formalism, the equations of motion are generated by extremizing a nonconservative action $\\mathcal{S}$, which is a functional of a doubled set of degrees of freedom. The corresponding nonconservative Lagrangian contains a potential $K$ which generates nonconservative forces and interactions. Such a nonconservative potential can arise in several ways, including from an open system interacting with inaccessible degrees of freedom or from integrating out or coarse-graining a subset of variables in closed systems. We generalize Noether's theorem to show how Noether currents are modified and no longer conserved when $K$ is non-...
Numerical study of chiral plasma instability within the classical statistical field theory approach
Buividovich, P V
2015-01-01
We report on a numerical study of the real-time dynamics of chirally imbalanced lattice Dirac fermions coupled to dynamical electromagnetic field. To this end we use the classical statistical field theory approach, in which the quantum evolution of fermions is simulated exactly, and electromagnetic fields are treated as classical. Motivated by recent experiments on chirally imbalanced Dirac semimetals, we use the Wilson-Dirac lattice Hamiltonian for fermions in order to model the emergent nature of chiral symmetry at low energies. In general, we observe that the backreaction of fermions on the electromagnetic field prevents the system from acquiring large chirality imbalance. In the case of chirality pumping in parallel electric and magnetic fields, electric field is screened by the produced on-shell fermions and the accumulation of chirality is hence stopped. In the case of evolution with initially present chirality imbalance, axial charge tends to decay at the expense of nonzero helicity of electromagnetic ...
Semenov, Alexander; Babikov, Dmitri
2014-01-16
For computational treatment of rotationally inelastic scattering of molecules, we propose to use the mixed quantum/classical theory, MQCT. The old idea of treating translational motion classically, while quantum mechanics is used for rotational degrees of freedom, is developed to the new level and is applied to Na + N2 collisions in a broad range of energies. Comparison with full-quantum calculations shows that MQCT accurately reproduces all, even minor, features of energy dependence of cross sections, except scattering resonances at very low energies. The remarkable success of MQCT opens up wide opportunities for computational predictions of inelastic scattering cross sections at higher temperatures and/or for polyatomic molecules and heavier quenchers, which is computationally close to impossible within the full-quantum framework.
Khrennikov, Andrei
2016-01-01
The scientific methodology based on two descriptive levels, ontic (reality as it is ) and epistemic (observational), is briefly presented. Following Schr\\"odinger, we point to the possible gap between these two descriptions. Our main aim is to show that, although ontic entities may be inaccessible for observations, they can be useful for clarification of the physical nature of operational epistemic entities. We illustrate this thesis by the concrete example: starting with the concrete ontic model preceding quantum mechanics (the latter is treated as an epistemic model), namely, prequantum classical statistical field theory (PCSFT), we propose the natural physical interpretation for the basic quantum mechanical entity - the quantum state ("wave function"). The correspondence PCSFT to QM is not straightforward, it couples the covariance operators of classical (prequantum) random fields with the quantum density operators. We use this correspondence to clarify the physical meaning of the pure quantum state and th...
An alternative formulation of classical electromagnetic duality
Li, K; Li, Kang; Naón, Carlos M.
2001-01-01
By introducing a doublet of electromagnetic four dimensional vector potentials, we set up a manifestly Lorentz covariant and SO(2) duality invariant classical field theory of electric and magnetic charges. In our formulation one does not need to introduce the concept of Dirac string.
The Postmodern Turn: Shall Classic Grounded Theory Take That Detour? A Review Essay
Directory of Open Access Journals (Sweden)
Vivian B. Martin, PhD
2006-06-01
Full Text Available Adherents to classic grounded theory have gotten used to spotting the pretenders working under the grounded theory banner. Some of these faux-GT researchers have worked in a fog, misunderstanding fundamentals of the method; these are the studies that leave us shaking our heads and wondering about the doctoral committee and peer reviewers who did not bother to find out more about the method they were evaluating. More infuriating are the authors who are claiming to improve on grounded theory, to reground it, to quote one notable British author who, lack of handson grounded theory experience aside, manages a booklength critique of the method. Two recent books in the“remaking grounded theory” genre are from sociologists with some years of grounded theory projects behind them. Adele E. Clarke, author of Situational Analysis, was a student and colleague of Anselm L. Strauss at the University of California San Francisco. Kathy Charmaz, author of Constructing Grounded Theory, is among the few grounded theorists who studied with Barney G. Glaser and Strauss at UCSF.
Classical Higgs fields on gauge gluon bundles
Directory of Open Access Journals (Sweden)
Palese Marcella
2016-01-01
Full Text Available Classical Higgs fields and related canonical conserved quantities are defined by invariant variational problems on suitably defined gauge gluon bundles. We consider Lagrangian field theories which are assumed to be invariant with respect to the action of a gauge-natural group. As an illustrative example we exploit the ‘gluon Lagrangian’, i.e. a Yang-Mills Lagrangian on the (1, 1-order gauge-natural bundle of SU(3-principal connections. The kernel of the gauge-natural Jacobi morphism for such a Lagrangian, by inducing a reductive split structure, canonically defines a ‘gluon classical Higgs field’.
Capri, M A L; Pereira, A D; Fiorentini, D; Guimaraes, M S; Mintz, B W; Palhares, L F; Sorella, S P
2016-01-01
In order to construct a gauge invariant two-point function in a Yang-Mills theory, we propose the use of the all-order gauge invariant transverse configurations A^h. Such configurations can be obtained through the minimization of the functional A^2_{min} along the gauge orbit within the BRST invariant formulation of the Gribov-Zwanziger framework recently put forward in [1,2] for the class of the linear covariant gauges. This correlator turns out to provide a characterization of non-perturbative aspects of the theory in a BRST invariant and gauge parameter independent way. In particular, it turns out that the poles of are the same as those of the transverse part of the gluon propagator, which are also formally shown to be independent of the gauge parameter entering the gauge condition through the Nielsen identities. The latter follow from the new exact BRST invariant formulation introduced before. Moreover, the correlator enables us to attach a BRST invariant meaning to the possible positivity violation of ...
Failure of classical traffic flow theories: Stochastic highway capacity and automatic driving
Kerner, Boris S
2016-01-01
In a mini-review [Physica A {\\bf 392} (2013) 5261--5282] it has been shown that classical traffic flow theories and models failed to explain empirical traffic breakdown -- a phase transition from metastable free flow to synchronized flow at highway bottlenecks. The main objective of this mini-review is to study the consequence of this failure of classical traffic-flow theories for an analysis of empirical stochastic highway capacity as well as for the effect of automatic driving vehicles and cooperative driving on traffic flow. To reach this goal, we show a deep connection between the understanding of empirical stochastic highway capacity and a reliable analysis of automatic driving vehicles in traffic flow. With the use of simulations in the framework of three-phase traffic theory, a probabilistic analysis of the effect of automatic driving vehicles on a mixture traffic flow consisting of a random distribution of automatic driving and manual driving vehicles has been made. We have found that the parameters o...
Failure of classical traffic flow theories: Stochastic highway capacity and automatic driving
Kerner, Boris S.
2016-05-01
In a mini-review Kerner (2013) it has been shown that classical traffic flow theories and models failed to explain empirical traffic breakdown - a phase transition from metastable free flow to synchronized flow at highway bottlenecks. The main objective of this mini-review is to study the consequence of this failure of classical traffic-flow theories for an analysis of empirical stochastic highway capacity as well as for the effect of automatic driving vehicles and cooperative driving on traffic flow. To reach this goal, we show a deep connection between the understanding of empirical stochastic highway capacity and a reliable analysis of automatic driving vehicles in traffic flow. With the use of simulations in the framework of three-phase traffic theory, a probabilistic analysis of the effect of automatic driving vehicles on a mixture traffic flow consisting of a random distribution of automatic driving and manual driving vehicles has been made. We have found that the parameters of automatic driving vehicles can either decrease or increase the probability of the breakdown. The increase in the probability of traffic breakdown, i.e., the deterioration of the performance of the traffic system can occur already at a small percentage (about 5%) of automatic driving vehicles. The increase in the probability of traffic breakdown through automatic driving vehicles can be realized, even if any platoon of automatic driving vehicles satisfies condition for string stability.
Energy Technology Data Exchange (ETDEWEB)
Lehnhart, B.C.
2007-05-15
This thesis is concerned with electromagnetic pion production within manifestly Lorentz-invariant chiral perturbation theory using the assumption of isospin symmetry. In a one-loop calculation up to the chiral order O(q{sup 4}), 105 Feynman diagrams contribute, consisting of 20 tree graphs and 85 loop diagrams. The tree graphs are classified as 16 pole diagrams and 4 contact graphs. Of the 85 loop diagrams, 50 diagrams are of order three and 35 diagrams are of fourth order. To calculate the pion production amplitude algorithms are developed on the basis of the Mathematica package FeynCalc. The one-photon-exchange approximation allows one to parametrise the pion production amplitude as the product of the polarisation vector of the (virtual) photon and the matrix element of the transition current. The polarisation vector is related to the leptonic vertex and the photon propagator and is well-known from QED. The dependence of the amplitude on the strong interaction is contained in the matrix element of the transition current, and we use chiral perturbation theory to describe this matrix element. The transition current can be expressed in terms of six gauge invariant amplitudes, each of which can again be decomposed into three isospin amplitudes. Linear combinations of these amplitudes allow us to describe the physical amplitudes. The one-loop integrals appearing within this calculation are determined numerically by the program LoopTools. In the case of tensorial integrals it is required to perform the method of Passarino and Veltman first. Furthermore, we apply the reformulated infrared regularisation which ensures that the results fulfill the chiral power counting. For this purpose algorithms are developed which determine the subtraction terms automatically. The obtained isospin amplitudes are integrated in the program MAID. As tests the s-wave multipoles E{sub 0+} and L{sub 0+} (using results up to chiral order O(q{sup 3})) are calculated in the threshold region
Inflation in a conformally invariant two-scalar-field theory with an extra R{sup 2} term
Energy Technology Data Exchange (ETDEWEB)
Bamba, Kazuharu [Fukushima University, Division of Human Support System, Faculty of Symbiotic Systems Science, Fukushima (Japan); Ochanomizu University, Leading Graduate School Promotion Center, Tokyo (Japan); Ochanomizu University, Department of Physics, Graduate School of Humanities and Sciences, Tokyo (Japan); Odintsov, Sergei D. [Institut de Ciencies de l' Espai (IEEC-CSIC), Barcelona (Spain); Institucio Catalana de Recerca i Estudis Avancats (ICREA), Barcelona (Spain); Tretyakov, Petr V. [Joined Institute for Nuclear Research, Dubna (Russian Federation)
2015-07-15
We explore inflationary cosmology in a theory where there are two scalar fields which non-minimally couple to the Ricci scalar and an additional R{sup 2} term, which breaks the conformal invariance. Particularly, we investigate the slow-roll inflation in the case of one dynamical scalar field and that of two dynamical scalar fields. It is explicitly demonstrated that the spectral index of the scalar mode of the density perturbations and the tensor-to-scalar ratio can be consistent with the observations obtained by the recent Planck satellite. The graceful exit from the inflationary stage is achieved as in convenient R{sup 2} gravity. We also propose the generalization of the model under discussion with three scalar fields. (orig.)
Inflation in a conformally invariant two-scalar-field theory with an extra R{sup 2} term
Energy Technology Data Exchange (ETDEWEB)
Bamba, Kazuharu, E-mail: bamba@sss.fukushima-u.ac.jp [Division of Human Support System, Faculty of Symbiotic Systems Science, Fukushima University, 960-1296, Fukushima (Japan); Leading Graduate School Promotion Center, Ochanomizu University, 112-8610, Tokyo (Japan); Department of Physics, Graduate School of Humanities and Sciences, Ochanomizu University, 112-8610, Tokyo (Japan); Odintsov, Sergei D. [Institut de Ciencies de lEspai (IEEC-CSIC), Campus UAB, Carrer de Can Magrans, s/n 08193 Cerdanyola del Valles, Barcelona (Spain); Institució Catalana de Recerca i Estudis Avançats (ICREA), Passeig Lluís Companys 23, 08010, Barcelona (Spain); Tretyakov, Petr V. [Joined Institute for Nuclear Research, Dubna, Moscow Region (Russian Federation)
2015-07-23
We explore inflationary cosmology in a theory where there are two scalar fields which non-minimally couple to the Ricci scalar and an additional R{sup 2} term, which breaks the conformal invariance. Particularly, we investigate the slow-roll inflation in the case of one dynamical scalar field and that of two dynamical scalar fields. It is explicitly demonstrated that the spectral index of the scalar mode of the density perturbations and the tensor-to-scalar ratio can be consistent with the observations obtaind by the recent Planck satellite. The graceful exit from the inflationary stage is achieved as in convenient R{sup 2} gravity. We also propose the generalization of the model under discussion with three scalar fields.
古典与新古典收入分配理论之比较%Comparisons on income distribution theories between classicism and neo-classicism
Institute of Scientific and Technical Information of China (English)
刘娟
2011-01-01
收入分配理论是经济学理论研究的基础,古典、新古典的收入分配研究是经济学理论研究基础之基础。价值理论决定了收入分配理论,本文主要从古典、新古典的价值理论入手,比较了其收入分配理论的不同并对其原因进行了分析。%Income distribution theory based on value theory is the basis of the economics study and classical and neo-classical income distribution research are the basis of the basis.This study compares differences between the two income distribution theories and a
for the applicability to classical conditioning of Premack’s reinforcement theory in which the rate of reinforced responding is determined in part by the precontingency rate of the response. (Author)
Geometric approach to chaos in the classical dynamics of abelian lattice gauge theory
Casetti, L; Pettini, M; Casetti, Lapo; Gatto, Raoul; Pettini, Marco
1998-01-01
A Riemannian geometrization of dynamics is used to study chaoticity in the classical Hamiltonian dynamics of a U(1) lattice gauge theory. This approach allows one to obtain analytical estimates of the largest Lyapunov exponent in terms of time averages of geometric quantities. These estimates are compared with the results of numerical simulations, and turn out to be very close to the values extrapolated for very large lattice sizes even when the geometric quantities are computed using small lattices. The scaling of the Lyapunov exponent with the energy density is found to be well described by a quadratic power law.
Geometric approach to chaos in the classical dynamics of Abelian lattice gauge theory
Energy Technology Data Exchange (ETDEWEB)
Casetti, Lapo [Istituto Nazionale per la Fisica della Materia (INFM), Unita di Ricerca del Politecnico di Torino, Dipartimento di Fisica, Politecnico di Torino, Turin (Italy); Gatto, Raoul [Departement de Physique Theorique, Universite de Geneve, Geneva (Switzerland); Pettini, Marco [Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi 5, Florence (Italy)
1999-04-23
A Riemannian geometrization of dynamics is used to study chaoticity in the classical Hamiltonian dynamics of a U(1) lattice gauge theory. This approach allows one to obtain analytical estimates of the largest Lyapunov exponent in terms of time averages of geometric quantities. These estimates are compared with the results of numerical simulations, and turn out to be very close to the values extrapolated for very large lattice sizes even when the geometric quantities are computed using small lattices. The scaling of the Lyapunov exponent {lambda} with the energy density {epsilon} is found to be well described by the law {lambda}{proportional_to}{epsilon}{sup 2}. (author)
Wave packet dynamics in energy space, random matrix theory, and the quantum-classical correspondence
Cohen; Izrailev; Kottos
2000-03-06
We apply random-matrix-theory (RMT) to the analysis of evolution of wave packets in energy space. We study the crossover from ballistic behavior to saturation, the possibility of having an intermediate diffusive behavior, and the feasibility of strong localization effect. Both theoretical considerations and numerical results are presented. Using quantal-classical correspondence considerations we question the validity of the emerging dynamical picture. In particular, we claim that the appearance of the intermediate diffusive behavior is possibly an artifact of the RMT strategy.
Redundancy of constraints in the classical and quantum theories of gravitation.
Moncrief, V.
1972-01-01
It is shown that in Dirac's version of the quantum theory of gravitation, the Hamiltonian constraints are greatly redundant. If the Hamiltonian constraint condition is satisfied at one point on the underlying, closed three-dimensional manifold, then it is automatically satisfied at every point, provided only that the momentum constraints are everywhere satisfied. This permits one to replace the usual infinity of Hamiltonian constraints by a single condition which may be taken in the form of an integral over the manifold. Analogous theorems are given for the classical Einstein Hamilton-Jacobi equations.
Peridynamic theory of solids from the perspective of classical statistical mechanics
Rahman, R.; Foster, J. T.
2015-11-01
In this paper the classical statistical mechanics has been explored in order to develop statistical mechanical framework for peridynamics. Peridynamic equation of motion is known as upscaled Newton's equation. The peridynamic system consists of finite number of nonlocally interacting particles at nano and meso scales. This particle representation of peridynamics can be treated in terms of classical statistical mechanics. Hence, in this work the phase space is constructed based on the PD particle from their evolving momentum pi and positions xi. The statistical ensembles are derived by defining appropriate partition functions. The algorithms for NVE and NPH implemented in the classical molecular dynamics are revisited for equilibrium peridynamic models. The current work introduces Langevin dynamics to the peridynamic theory through fluctuation-dissipation principle. This introduces a heat bath to the peridynamic system which eliminates the ambiguity with the role of temperature in a peridynamic system. Finally, it was seen that the homogenization of a peridynamic model with finite number of particles approaches to a conventional continuum model. The upscaled non-equilibrium peridynamics has potential applications in modeling wide variety of multiscale-multiphysics problems from nano to macro scale or vice versa.
The Super-Natural Supersymmetry and Its Classic Example: M-Theory Inspired NMSSM
Li, Tianjun; Wang, Xiao-Chuan
2015-01-01
We briefly review the super-natural supersymmetry (SUSY), which provides a most promising solution to the SUSY electroweak fine-tuning problem. In particular, we address its subtle issues as well. Unlike the Minimal Supersymmetric Standard model (MSSM), the Next to MSSM (NMSSM) can be scale invariant and has no mass parameter in its Lagrangian before SUSY and gauge symmetry breakings. Therefore, the NMSSM is a perfect framework for super-natural SUSY. To give the SUSY breaking soft mass to the singlet, we consider the moduli and dilaton dominant SUSY breaking scenarios in M-theory on $S^1/Z_2$. In these scenarios, SUSY is broken by one and only one $F$-term of moduli or dilaton, and the SUSY breaking soft terms can be determined via the K\\"ahler potential and superpotential from Calabi-Yau compactification of M-theory on $S^1/Z_2$. Thus, as predicted by super-natural SUSY, the SUSY electroweak fine-tuning measure is of unity order. In the moduli dominant SUSY breaking scenario, the right-handed sleptons are r...
Demythologizing the machine: Patrick Geddes, Lewis Mumford, and classical sociological theory.
Renwick, Chris; Gunn, Richard C
2008-01-01
This paper reconsiders the work of the Scottish biologist, sociologist, and town planner Patrick Geddes and his most famous intellectual disciple: the American independent scholar Lewis Mumford. It is argued that existing interpretations of their work, ranging from a dismissal of the two men as eccentric polymaths to the speculative emphasis on the importance of psychological theories in Mumford's oeuvre, are fundamentally flawed. Examining their writings and the letters they exchanged during their 17-year correspondence, this paper shows that the only way we can appreciate the scholarly conventions underpinning Geddes's and Mumford's work, as well as the context in which it was produced, is by looking to the principles of classical sociological theory.
Mahajan, Gaurang
2007-01-01
The quantum theory of a harmonic oscillator with a time dependent frequency arises in several important physical problems, especially in the study of quantum field theory in an external background. While the mathematics of this system is straightforward, several conceptual issues arise in such a study. We present a general formalism to address some of the conceptual issues like the emergence of classicality, definition of particle content, back reaction etc. In particular, we parametrize the wave function in terms of a complex number (which we call excitation parameter) and express all physically relevant quantities in terms it. Many of the notions -- like those of particle number density, effective Lagrangian etc., which are usually defined using asymptotic in-out states -- are generalized as time-dependent concepts and we show that these generalized definitions lead to useful and reasonable results. Having developed the general formalism we apply it to several examples. Exact analytic expressions are found ...
Classical R-matrix theory for bi-Hamiltonian field systems
Energy Technology Data Exchange (ETDEWEB)
Blaszak, Maciej [Department of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznan (Poland); Szablikowski, Blazej M [Department of Mathematics, University of Glasgow, Glasgow G12 8QW (United Kingdom)], E-mail: blaszakm@amu.edu.pl, E-mail: b.szablikowski@maths.gla.ac.uk
2009-10-09
This is a survey of the application of the classical R-matrix formalism to the construction of infinite-dimensional integrable Hamiltonian field systems. The main point is the study of bi-Hamiltonian structures. Appropriate constructions on Poisson, noncommutative and loop algebras as well as the central extension procedure are presented. The theory is developed for (1 + 1)- and (2 + 1)-dimensional field and lattice soliton systems as well as hydrodynamic systems. The formalism presented contains sufficiently many proofs and important details to make it self-contained and complete. The general theory is applied to several infinite-dimensional Lie algebras in order to construct both dispersionless and dispersive (soliton) integrable field systems.
Renormalized kinetic theory of classical fluids in and out of equilibrium
Daligault, Jerome
2011-01-01
We present a theory for the construction of renormalized kinetic equations to describe the dynamics of classical systems of particles in or out of equilibrium. A closed, self-consistent set of evolution equations is derived for the single-particle phase-space distribution function $f$, the correlation function $C=$, the retarded and advanced density response functions $\\chi^{R,A}=\\delta f/\\delta\\phi$ to an external potential $\\phi$, and the associated memory functions $\\Sigma^{R,A,C}$. The basis of the theory is an effective action functional $\\Omega$ of external potentials $\\phi$ that contains all information about the dynamical properties of the system. In particular, its functional derivatives generate successively the single-particle phase-space density $f$ and all the correlation and density response functions, which are coupled through an infinite hierarchy of evolution equations. Traditional renormalization techniques are then used to perform the closure of the hierarchy through memory functions. The l...
Equivariant Semi-topological Invariants, Atiyah's KR-theory, and Real Algebraic Cycles
Heller, Jeremiah
2010-01-01
We establish an Atiyah-Hirzebruch type spectral sequence relating real morphic cohomology and real semi-topological K-theory and prove it to be compatible with the Atiyah-Hirzebruch spectral sequence relating Bredon cohomology and Atiyah's KR-theory constructed by Dugger. An equivariant and a real version of Suslin's conjecture on morphic cohomology are formulated, proved to come from the complex version of Suslin conjecture and verified for certain real varieties. In conjunction with the spectral sequences constructed here this allows the computation of the real semi-topological K-theory of some real varieties. As another application of this spectral sequence we give an alternate proof of the Lichtenbaum-Quillen conjecture over $\\R$, extending an earlier proof of Karoubi and Weibel.
Observables in classical canonical gravity: folklore demystified
Pons, J M; Sundermeyer, K A
2010-01-01
We give an overview of some conceptual difficulties, sometimes called paradoxes, that have puzzled for years the physical interpetation of classical canonical gravity and, by extension, the canonical formulation of generally covariant theories. We identify these difficulties as stemming form some terminological misunderstandings as to what is meant by "gauge invariance", or what is understood classically by a "physical state". We make a thorough analysis of the issue and show that all purported paradoxes disappear when the right terminology is in place. Since this issue is connected with the search of observables - gauge invariant quantities - for these theories, we formally show that time evolving observables can be constructed for every observer. This construction relies on the fixation of the gauge freedom of diffeomorphism invariance by means of a scalar coordinatization. We stress the condition that the coordinatization must be made with scalars. As an example of our method for obtaining observables we d...
Directory of Open Access Journals (Sweden)
Jesús García-de-Madariaga
2011-10-01
Full Text Available There has been a lot of discussion about corporate social responsibility (CSR during these last decades. Neoclassical authors support the idea that CSR is not compatible with the objective of profit maximization, and defenders of CSR argue that, in these times of globalization and network economies, the idea of a company managed just to meet shareholders’ interests does not support itself. However, beyond this discussion, how can CSR affect firms’ market value? If we found a positive relationship between these variables, we could conclude that the two theories are reconcilable and the objective of profit maximization, perhaps, should satisfy not only shareholders’ interests, but also stakeholders’. We review previous literature and propose a model to analyze how CSR affects firms’ market value.
Manifestly scale-invariant regularization and quantum effective operators
Ghilencea, D.M.
2016-01-01
Scale invariant theories are often used to address the hierarchy problem, however the regularization of their quantum corrections introduces a dimensionful coupling (dimensional regularization) or scale (Pauli-Villars, etc) which break this symmetry explicitly. We show how to avoid this problem and study the implications of a manifestly scale invariant regularization in (classical) scale invariant theories. We use a dilaton-dependent subtraction function $\\mu(\\sigma)$ which after spontaneous breaking of scale symmetry generates the usual DR subtraction scale $\\mu(\\langle\\sigma\\rangle)$. One consequence is that "evanescent" interactions generated by scale invariance of the action in $d=4-2\\epsilon$ (but vanishing in $d=4$), give rise to new, finite quantum corrections. We find a (finite) correction $\\Delta U(\\phi,\\sigma)$ to the one-loop scalar potential for $\\phi$ and $\\sigma$, beyond the Coleman-Weinberg term. $\\Delta U$ is due to an evanescent correction ($\\propto\\epsilon$) to the field-dependent masses (of...
RIKEN BNL RESEARCH CENTER WORKSHOP ON GAUGE-INVARIANT VARIABLES IN GAUGE THEORIES, VOLUME 20
Energy Technology Data Exchange (ETDEWEB)
VAN BAAL,P.; ORLAND,P.; PISARSKI,R.
2000-06-01
This four-day workshop focused on the wide variety of approaches to the non-perturbative physics of QCD. The main topic was the formulation of non-Abelian gauge theory in orbit space, but some other ideas were discussed, in particular the possible extension of the Maldacena conjecture to nonsupersymmetric gauge theories. The idea was to involve most of the participants in general discussions on the problem. Panel discussions were organized to further encourage debate and understanding. Most of the talks roughly fell into three categories: (1) Variational methods in field theory; (2) Anti-de Sitter space ideas; (3) The fundamental domain, gauge fixing, Gribov copies and topological objects (both in the continuum and on a lattice). In particular some remarkable progress in three-dimensional gauge theories was presented, from the analytic side by V.P. Nair and mostly from the numerical side by O. Philipsen. This work may ultimately have important implications for RHIC experiments on the high-temperature quark-gluon plasma.
Gusynin, VP; Khveshchenko, DV; Reenders, M
2003-01-01
We use the radial gauge to calculate the recently proposed ansatz for the physical electron propagator in such effective models of strongly correlated electron systems as the QED(3) theory of the pseudogap phase of the cuprates. The results of our analysis help to settle the recent dispute about the
H. Bleichrodt (Han); J.N. Doctor (Jason); M. Filko (Martin); P.P. Wakker (Peter)
2011-01-01
textabstractUtility independence is a central condition in multiattribute utility theory, where attributes of outcomes are aggregated in the context of risk. The aggregation of attributes in the absence of risk is studied in conjoint measurement. In conjoint measurement, standard sequences have been
The Quench Map in an Integrable Classical Field Theory: Nonlinear Schr\\"odinger Equation
Caudrelier, Vincent
2016-01-01
We study the non-equilibrium dynamics obtained by an abrupt change (a {\\em quench}) in the parameters of an integrable classical field theory, the nonlinear Schr\\"odinger equation. We first consider explicit one-soliton examples, which we fully describe by solving the direct part of the inverse scattering problem. We then develop some aspects of the general theory using elements of the inverse scattering method. For this purpose, we introduce the {\\em quench map} which acts on the space of scattering data and represents the change of parameter with fixed field configuration (initial condition). We describe some of its analytic properties by implementing a higher level version of the inverse scattering method, and we discuss the applications of Darboux-B\\"acklund transformations, Gelfand-Levitan-Marchenko equations and the Rosales series solution to a related, dual quench problem. Finally, we comment on the interplay between quantum and classical tools around the theme of quenches and on the usefulness of the ...
Directory of Open Access Journals (Sweden)
V. I. Khvorostyanov
2012-03-01
Full Text Available A new analytical parameterization of homogeneous ice nucleation is developed based on extended classical nucleation theory including new equations for the critical radii of the ice germs, free energies and nucleation rates as the functions of the temperature and water saturation ratio simultaneously. By representing these quantities as separable products of the analytical functions of the temperature and supersaturation, analytical solutions are found for the integral-differential supersaturation equation and concentration of nucleated crystals. Parcel model simulations are used to illustrate the general behavior of various nucleation properties under various conditions, for justifications of the further key analytical simplifications, and for verification of the resulting parameterization.
The final parameterization is based upon the values of the supersaturation that determines the current or maximum concentrations of the nucleated ice crystals. The crystal concentration is analytically expressed as a function of time and can be used for parameterization of homogeneous ice nucleation both in the models with small time steps and for substep parameterization in the models with large time steps. The crystal concentration is expressed analytically via the error functions or elementary functions and depends only on the fundamental atmospheric parameters and parameters of classical nucleation theory. The diffusion and kinetic limits of the new parameterization agree with previous semi-empirical parameterizations.
Gauge invariant Lagrangian formulation of higher spin massive bosonic field theory in AdS space
Buchbinder, I L; Lavrov, P M
2006-01-01
We develop the BRST approach to Lagrangian construction for the massive integer higher spin fields in an arbitrary dimensional AdS space. The theory is formulated in terms of auxiliary Fock space. Closed nonlinear symmetry algebra of higher spin bosonic theory in AdS space is found and method of deriving the BRST operator for such an algebra is proposed. General procedure of Lagrangian construction describing the dynamics of bosonic field with any spin is given on the base of the BRST operator. No off-shell constraints on the fields and the gauge parameters are used from the very beginning. As an example of general procedure, we derive the Lagrangians for massive bosonic fields with spin 0, 1 and 2 containing total set of auxiliary fields and gauge symmetries.
Gauge invariant Lagrangian formulation of higher spin massive bosonic field theory in AdS space
Energy Technology Data Exchange (ETDEWEB)
Buchbinder, I.L. [Department of Theoretical Physics, Tomsk State Pedagogical University, Tomsk 634041 (Russian Federation)]. E-mail: joseph@tspu.edu.ru; Krykhtin, V.A. [Laboratory of Mathematical Physics, Tomsk Polytechnic University, Tomsk 634034 (Russian Federation)]. E-mail: krykhtin@mph.phtd.tpu.edu.ru; Lavrov, P.M. [Department of Mathematical Analysis, Tomsk State Pedagogical University, Tomsk 634041 (Russian Federation)]. E-mail: lavrov@tspu.edu.ru
2007-02-05
In this work we develop the BRST approach to Lagrangian construction for the massive integer higher spin fields in an arbitrary dimensional AdS space. The theory is formulated in terms of auxiliary Fock space. Closed nonlinear symmetry algebra of higher spin bosonic theory in AdS space is found and a method of deriving the BRST operator for such an algebra is proposed. A general procedure of Lagrangian construction, describing the dynamics of a bosonic field with any spin is given on the base of the BRST operator. No off-shell constraints on the fields and the gauge parameters are used from the very beginning. As an example of general procedure, we derive the Lagrangians for massive bosonic fields with spin 0, 1 and 2, containing the total set of auxiliary fields and gauge symmetries.
Gauge and supersymmetry invariance of N = 2 boundary Chern-Simons theory
Faizal, Mir; Luo, Yuan; Smith, Douglas J.; Tan, Meng-Chwan; Zhao, Qin
2017-01-01
In this paper, we study the restoration of gauge symmetry and up to half the supersymmetry (N = (2 , 0) or N = (1 , 1) in two dimensions) for N = 2 non-Abelian Chern-Simons theories in the presence of a boundary. We describe the boundary action which is a supersymmetric WZW model coupled to the bulk Chern-Simons theory. Unlike the N = 1 case, higher supersymmetry (N = (2 , 0)) will endow the group manifold of the WZW model with a complex structure. Therefore, the N = (2 , 0) WZW model in our paper is constructed via a coset space Gc / G, where G is the same as the gauge group in the Chern-Simons action.
Higgs-Yukawa model in chirally-invariant lattice field theory
Energy Technology Data Exchange (ETDEWEB)
Bulava, John [CERN, Geneva (Switzerland). Physics Department; Gerhold, Philipp; Kallarackal, Jim; Nagy, Attila [Humboldt Univ. Berlin (Germany). Inst. fuer Physik; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Knippschild, Bastian [National Taiwan Univ., Taipei (China). Dept. of Physics; Lin, C.J. David [National Chiao-Tung Univ., Hsinchu (China). Inst. of Physics; National Centre for Theoretical Sciences, Hsinchu (China). Div. of Physics; Nagai, Kei-Ichi [Nagoya Univ., Nagoya, Aichi (Japan). Kobayashi-Maskawa Institute; Ogawa, Kenji [Chung-Yuan Christian Univ., Chung-Li (China). Dept. of Physics
2012-10-15
Non-perturbative numerical lattice studies of the Higgs-Yukawa sector of the standard model with exact chiral symmetry are reviewed. In particular, we discuss bounds on the Higgs boson mass at the standard model top quark mass, and in the presence of heavy fermions. We present a comprehensive study of the phase structure of the theory at weak and very strong values of the Yukawa coupling as well as at non-zero temperature.
Gauge-invariant extensions of the Proca model in a noncommutative space-time
Abreu, Everton M. C.; Neto, Jorge Ananias; Fernandes, Rafael L.; Mendes, Albert C. R.
2016-09-01
The gauge invariance analysis of theories described in noncommutative (NC) space-times can lead us to interesting results since noncommutativity is one of the possible paths to investigate quantum effects in classical theories such as general relativity, for example. This theoretical possibility has motivated us to analyze the gauge invariance of the NC version of the Proca model, which is a second-class system, in Dirac’s classification, since its classical formulation (commutative space-time) has its gauge invariance broken thanks to the mass term. To obtain such gauge invariant model, we have used the gauge unfixing method to construct a first-class NC version of the Proca model. We have also questioned if the gauge symmetries of NC theories are affected necessarily or not by the NC parameter. In this way, we have calculated its respective symmetries in a standard way via Poisson brackets.
Gauge-invariant extensions of the Proca model in a noncommutative space-time
Abreu, Everton M C; Fernandes, Rafael L; Mendes, Albert C R
2016-01-01
The gauge invariance analysis of theories described in noncommutative (NC) space-times can lead us to interesting results since noncommutativity is one of the possible paths to investigate quantum effects in classical theories such as general relativity, for example. This theoretical possibility has motivated us to analyze the gauge invariance of the NC version of the Proca model, which is a second-class system, in Dirac's classification, since its classical formulation (commutative space-time) has its gauge invariance broken thanks to the mass term. To obtain such gauge invariant model, we have used the gauge unfixing method to construct a first-class NC version of the Proca model. We have also questioned if the gauge symmetries of NC theories, are affected necessarily or not by the NC parameter. In this way, we have calculated its respective symmetries in a standard way via Poisson brackets.
Dumas, H Scott
2014-01-01
This is a semi-popular mathematics book aimed at a broad readership of mathematically literate scientists, especially mathematicians and physicists who are not experts in classical mechanics or KAM theory, and scientific-minded readers. Parts of the book should also appeal to less mathematically trained readers with an interest in the history or philosophy of science. The scope of the book is broad: it not only describes KAM theory in some detail, but also presents its historical context (thus showing why it was a 'breakthrough'). Also discussed are applications of KAM theory (especially to celestial mechanics and statistical mechanics) and the parts of mathematics and physics in which KAM theory resides (dynamical systems, classical mechanics, and Hamiltonian perturbation theory). Although a number of sources on KAM theory are now available for experts, this book attempts to fill a long-standing gap at a more descriptive level. It stands out very clearly from existing publications on KAM theory because it ...
Haataja, Mikko; Gránásy, László; Löwen, Hartmut
2010-08-01
Herein we provide a brief summary of the background, events and results/outcome of the CECAM workshop 'Classical density functional theory methods in soft and hard matter held in Lausanne between October 21 and October 23 2009, which brought together two largely separately working communities, both of whom employ classical density functional techniques: the soft-matter community and the theoretical materials science community with interests in phase transformations and evolving microstructures in engineering materials. After outlining the motivation for the workshop, we first provide a brief overview of the articles submitted by the invited speakers for this special issue of Journal of Physics: Condensed Matter, followed by a collection of outstanding problems identified and discussed during the workshop. 1. Introduction Classical density functional theory (DFT) is a theoretical framework, which has been extensively employed in the past to study inhomogeneous complex fluids (CF) [1-4] and freezing transitions for simple fluids, amongst other things. Furthermore, classical DFT has been extended to include dynamics of the density field, thereby opening a new avenue to study phase transformation kinetics in colloidal systems via dynamical DFT (DDFT) [5]. While DDFT is highly accurate, the computations are numerically rather demanding, and cannot easily access the mesoscopic temporal and spatial scales where diffusional instabilities lead to complex solidification morphologies. Adaptation of more efficient numerical methods would extend the domain of DDFT towards this regime of particular interest to materials scientists. In recent years, DFT has re-emerged in the form of the so-called 'phase-field crystal' (PFC) method for solid-state systems [6, 7], and it has been successfully employed to study a broad variety of interesting materials phenomena in both atomic and colloidal systems, including elastic and plastic deformations, grain growth, thin film growth, solid
The classical electromagnetic field
Eyges, Leonard
2010-01-01
This excellent text covers a year's course in advanced theoretical electromagnetism, first introducing theory, then its application. Topics include vectors D and H inside matter, conservation laws for energy, momentum, invariance, form invariance, covariance in special relativity, and more.
Exact invariants and adiabatic invariants of the singular Lagrange system
Institute of Scientific and Technical Information of China (English)
陈向炜; 李彦敏
2003-01-01
Based on the theory of symmetries and conserved quantities of the singular Lagrange system,the perturbations to the symmetries and adiabatic invariants of the singular Lagrange systems are discussed.Firstly,the concept of higher-order adiabatic invariants of the singular Lagrange system is proposed.Then,the conditions for the existence of the exact invariants and adiabatic invariants are proved,and their forms are given.Finally,an example is presented to illustrate these results.
Self psychology as a shift away from the paranoid strain in classical analytic theory.
Terman, David M
2014-12-01
Classical psychoanalytic theory has a paranoid strain. There is, in effect, an "evil other"--the id--within each individual that must be tamed in development and confronted and worked through as resistance in treatment. This last has historically endgendered an adversarial relationship between patient and analyst. This paranoid strain came from a paranoid element in Freud's personality that affected his worldview, his relationships, and his theory. Self psychology offers a different view of development and conflict. It stresses the child's need for responsiveness from and admiration of caretakers in order to develop a well-functioning self. Though severe behavioral and character problems may result from faults in the process of self-construction, the essential need is not instinctual discharge but connection. Hence the long-assumed opposition between individual needs and social institutions or between patient and analyst is no longer inevitable or universal. Rather, an understanding of the primary need for connection creates both a different interpretive stance and a more cooperative ambience. These changes in theory and technique are traced to Kohut's personal struggles to emancipate himself from his paranoid mother.
Nakamura, Kouji
2008-01-01
Some formulae for the perturbations of the matter fields are summarized within the framework of the second-order gauge-invariant cosmological perturbation theory in a four dimensional homogeneous isotropic universe, which is developed in the papers [K. Nakamura, Prog. Theor. Phys. {\\bf 117} (2005), 17.]. We derive the formulae for the perturbations of the energy momentum tensors and equations of motion in the cases of a perfect fluid, an imperfect fluid, and a signle scalar field, and show that all equations are derived in terms of gauge-invariant variables without any gauge fixing.
Vacuum Radiation and Symmetry Breaking in Conformally Invariant Quantum Field Theory
Aldaya, V; Cerveró, J M
1999-01-01
The underlying reasons for the difficulty of unitarily implementing the whole conformal group $SO(4,2)$ in a massless Quantum Field Theory (QFT) are investigated in this paper. Firstly, we demonstrate that the singular action of the subgroup of special conformal transformations (SCT), on the standard Minkowski space $M$, cannot be primarily associated with the vacuum radiation problems, the reason being more profound and related to the dynamical breakdown of part of the conformal symmetry (the SCT subgroup, to be more precise) when representations of null mass are selected inside the representations of the whole conformal group. Then we show how the vacuum of the massless QFT radiates under the action of SCT (usually interpreted as transitions to a uniformly accelerated frame) and we calculate exactly the spectrum of the outgoing particles, which proves to be a generalization of the Planckian one, this recovered as a given limit.
Supernatural supersymmetry and its classic example: M-theory inspired NMSSM
Li, Tianjun; Raza, Shabbar; Wang, Xiao-Chuan
2016-06-01
We briefly review the supernatural supersymmetry (SUSY), which provides a most promising solution to the SUSY electroweak fine-tuning problem. In particular, we address its subtle issues as well. Unlike the minimal supersymmetric standard model (MSSM), the next to MSSM (NMSSM) can be scale invariant and has no mass parameter in its Lagrangian before SUSY and gauge symmetry breakings. Therefore, the NMSSM is a perfect framework for supernatural SUSY. To give the SUSY breaking soft mass to the singlet, we consider the moduli and dilaton dominant SUSY breaking scenarios in M-theory on S1/Z2. In these scenarios, SUSY is broken by one and only one F term of moduli or dilaton, and the SUSY breaking soft terms can be determined via the Kähler potential and superpotential from Calabi-Yau compactification of M-theory on S1/Z2. Thus, as predicted by supernatural SUSY, the SUSY electroweak fine-tuning measure is of unity order. In the moduli dominant SUSY breaking scenario, the right-handed sleptons are relatively light around 1 TeV, stau can even be as light as 580 GeV and degenerate with the lightest neutralino, chargino masses are larger than 1 TeV, the light stop masses are around 2 TeV or larger, the first two-generation squark masses are about 3 TeV or larger, and gluinos are heavier tha.n squarks. In the dilaton dominant SUSY breaking scenario, the qualitative picture remains the same but we have heavier spectra as compared to the moduli dominant SUSY breaking scenario. In addition to it, we have Higgs H2/A1-resonance solutions for dark matter (DM). In both scenarios, the minimal value of DM relic density is about 0.2. To obtain the observed DM relic density, we can consider the dilution effect from supercritical string cosmology or introduce the axino as the lightest supersymmetric particle.
Chandrasekhar limit: an elementary approach based on classical physics and quantum theory
Pinochet, Jorge; Van Sint Jan, Michael
2016-05-01
In a brief article published in 1931, Subrahmanyan Chandrasekhar made public an important astronomical discovery. In his article, the then young Indian astrophysicist introduced what is now known as the Chandrasekhar limit. This limit establishes the maximum mass of a stellar remnant beyond which the repulsion force between electrons due to the exclusion principle can no longer stop the gravitational collapse. In the present article, we create an elemental approximation to the Chandrasekhar limit, accessible to non-graduate science and engineering students. The article focuses especially on clarifying the origins of Chandrasekhar’s discovery and the underlying physical concepts. Throughout the article, only basic algebra is used as well as some general notions of classical physics and quantum theory.
Jeanmairet, Guillaume; Levesque, Maximilien; Rotenberg, Benjamin; Borgis, Daniel
2014-01-01
We report here how the hydration of complex surfaces can be efficiently studied thanks to recent advances in classical molecular density functional theory. This is illustrated on the example of the pyrophylite clay. After presenting the most recent advances, we show that the strength of this implicit method is that (i) it is in quantitative or semi-quantitative agreement with reference all-atoms simulations (molecular dynamics here) for both the solvation structure and energetics, and that (ii) the computational cost is two to three orders of magnitude less than in explicit methods. The method remains imperfect, in that it locally overestimates the polarization of water close to hydrophylic sites of the clay. The high numerical efficiency of the method is illustrated and exploited to carry a systematic study of the electrostatic and van der Waals components of the surface-solvant interactions within the most popular force field for clays, CLAYFF. Hydration structure and energetics are found to weakly depend u...
Classical solutions in quantum field theory solitons and instantons in high energy physics
Weinberg, Erick J
2012-01-01
Classical solutions play an important role in quantum field theory, high energy physics and cosmology. Real-time soliton solutions give rise to particles, such as magnetic monopoles, and extended structures, such as domain walls and cosmic strings, that have implications for early universe cosmology. Imaginary-time Euclidean instantons are responsible for important nonperturbative effects, while Euclidean bounce solutions govern transitions between metastable states. Written for advanced graduate students and researchers in elementary particle physics, cosmology and related fields, this book brings the reader up to the level of current research in the field. The first half of the book discusses the most important classes of solitons: kinks, vortices and magnetic monopoles. The cosmological and observational constraints on these are covered, as are more formal aspects, including BPS solitons and their connection with supersymmetry. The second half is devoted to Euclidean solutions, with particular emphasis on ...
Tractors, Mass and Weyl Invariance
Gover, A R; Waldron, A
2008-01-01
Deser and Nepomechie established a relationship between masslessness and rigid conformal invariance by coupling to a background metric and demanding local Weyl invariance, a method which applies neither to massive theories nor theories which rely upon gauge invariances for masslessness. We extend this method to describe massive and gauge invariant theories using Weyl invariance. The key idea is to introduce a new scalar field which is constant when evaluated at the scale corresponding to the metric of physical interest. This technique relies on being able to efficiently construct Weyl invariant theories. This is achieved using tractor calculus--a mathematical machinery designed for the study of conformal geometry. From a physics standpoint, this amounts to arranging fields in multiplets with respect to the conformal group but with novel Weyl transformation laws. Our approach gives a mechanism for generating masses from Weyl weights. Breitenlohner--Freedman stability bounds for Anti de Sitter theories arise na...
Tractors, mass, and Weyl invariance
Gover, A. R.; Shaukat, A.; Waldron, A.
2009-05-01
Deser and Nepomechie established a relationship between masslessness and rigid conformal invariance by coupling to a background metric and demanding local Weyl invariance, a method which applies neither to massive theories nor theories which rely upon gauge invariances for masslessness. We extend this method to describe massive and gauge invariant theories using Weyl invariance. The key idea is to introduce a new scalar field which is constant when evaluated at the scale corresponding to the metric of physical interest. This technique relies on being able to efficiently construct Weyl invariant theories. This is achieved using tractor calculus—a mathematical machinery designed for the study of conformal geometry. From a physics standpoint, this amounts to arranging fields in multiplets with respect to the conformal group but with novel Weyl transformation laws. Our approach gives a mechanism for generating masses from Weyl weights. Breitenlohner-Freedman stability bounds for Anti-de Sitter theories arise naturally as do direct derivations of the novel Weyl invariant theories given by Deser and Nepomechie. In constant curvature spaces, partially massless theories—which rely on the interplay between mass and gauge invariance—are also generated by our method. Another simple consequence is conformal invariance of the maximal depth partially massless theories. Detailed examples for spins s⩽2 are given including tractor and component actions, on-shell and off-shell approaches and gauge invariances. For all spins s⩾2 we give tractor equations of motion unifying massive, massless, and partially massless theories.
Sundararaman, Ravishankar
2014-01-01
Classical density-functional theory provides an efficient alternative to molecular dynamics simulations for understanding the equilibrium properties of inhomogeneous fluids. However, application of density-functional theory to multi-site molecular fluids has so far been limited by complications due to the implicit molecular geometry constraints on the site densities, whose resolution typically requires expensive Monte Carlo methods. Here, we present a general scheme of circumventing this so-called inversion problem: compressed representations of the orientation density. This approach allows us to combine the superior iterative convergence properties of multipole representations of the fluid configuration with the improved accuracy of site-density functionals. Next, from a computational perspective, we show how to extend the DFT++ algebraic formulation of electronic density-functional theory to the classical fluid case and present a basis-independent discretization of our formulation for molecular classical de...
Kalinin, A. V.; Grigor'ev, E. E.; Zhidkov, A. A.; Terent'ev, A. M.
2014-04-01
We study a one-dimensional stationary system of equations comprising the continuity equation for the ion concentration with the recombination effects taken into account and the Gauss law for the electric field. This system gives a simplified description of various phenomena in ionized medium theory and is used, in particular, for modeling of the electrode effect in the atmospheric surface layers with the turbulent diffusion effects neglected. Using the integral of the system and a phase portrait in the ion concentration plane, we offer a complete classification of types of solutions of the system, examine their properties, and deduce some analytical relations between the ion concentration and the electric field. The basic equations of classical electrode effect theory are obtained for some classes of solutions within the framework of this approach. Correct formulations of the problems are discussed. New classes of solutions, for which there are layers with infinitely increasing conductivity and charge density are described. The Appendix illustrates, in both analytical and graphical form, the results obtained in the main part of this paper on the basis of qualitative reasoning for parameters close to real. Analytical expressions for the fields and ion concentrations are given for all types of solutions. Relations for the distances between electrodes and analytical relations describing the properties of the spatially localized solutions are presented.
Field theory and weak Euler-Lagrange equation for classical particle-field systems.
Qin, Hong; Burby, Joshua W; Davidson, Ronald C
2014-10-01
It is commonly believed as a fundamental principle that energy-momentum conservation of a physical system is the result of space-time symmetry. However, for classical particle-field systems, e.g., charged particles interacting through self-consistent electromagnetic or electrostatic fields, such a connection has only been cautiously suggested. It has not been formally established. The difficulty is due to the fact that the dynamics of particles and the electromagnetic fields reside on different manifolds. We show how to overcome this difficulty and establish the connection by generalizing the Euler-Lagrange equation, the central component of a field theory, to a so-called weak form. The weak Euler-Lagrange equation induces a new type of flux, called the weak Euler-Lagrange current, which enters conservation laws. Using field theory together with the weak Euler-Lagrange equation developed here, energy-momentum conservation laws that are difficult to find otherwise can be systematically derived from the underlying space-time symmetry.
Statistical analysis of 4 types of neck whiplash injuries based on classical meridian theory.
Chen, Yemeng; Zhao, Yan; Xue, Xiaolin; Li, Hui; Wu, Xiuyan; Zhang, Qunce; Zheng, Xin; Wang, Tianfang
2015-01-01
As one component of the Chinese medicine meridian system, the meridian sinew (Jingjin, (see text), tendino-musculo) is specially described as being for acupuncture treatment of the musculoskeletal system because of its dynamic attributes and tender point correlations. In recent decades, the therapeutic importance of the sinew meridian has become revalued in clinical application. Based on this theory, the authors have established therapeutic strategies of acupuncture treatment in Whiplash-Associated Disorders (WAD) by categorizing four types of neck symptom presentations. The advantage of this new system is to make it much easier for the clinician to find effective acupuncture points. This study attempts to prove the significance of the proposed therapeutic strategies by analyzing data collected from a clinical survey of various WAD using non-supervised statistical methods, such as correlation analysis, factor analysis, and cluster analysis. The clinical survey data have successfully verified discrete characteristics of four neck syndromes, based upon the range of motion (ROM) and tender point location findings. A summary of the relationships among the symptoms of the four neck syndromes has shown the correlation coefficient as having a statistical significance (P syndrome factors are more related to the Liver, as originally described in classical theory. The hypothesis of meridian sinew syndromes in WAD is clearly supported by the statistical analysis of the clinical trials. This new discovery should be beneficial in improving therapeutic outcomes.
Structure Theory for Extended Kepler-Coulomb 3D Classical Superintegrable Systems
Directory of Open Access Journals (Sweden)
Ernie G. Kalnins
2012-06-01
Full Text Available The classical Kepler-Coulomb system in 3 dimensions is well known to be 2nd order superintegrable, with a symmetry algebra that closes polynomially under Poisson brackets. This polynomial closure is typical for 2nd order superintegrable systems in 2D and for 2nd order systems in 3D with nondegenerate (4-parameter potentials. However the degenerate 3-parameter potential for the 3D extended Kepler-Coulomb system (also 2nd order superintegrable is an exception, as its quadratic symmetry algebra doesn't close polynomially. The 3D 4-parameter potential for the extended Kepler-Coulomb system is not even 2nd order superintegrable. However, Verrier and Evans (2008 showed it was 4th order superintegrable, and Tanoudis and Daskaloyannis (2011 showed that in the quantum case, if a second 4th order symmetry is added to the generators, the double commutators in the symmetry algebra close polynomially. Here, based on the Tremblay, Turbiner and Winternitz construction, we consider an infinite class of classical extended Kepler-Coulomb 3- and 4-parameter systems indexed by a pair of rational numbers (k_1,k_2 and reducing to the usual systems when k_1=k_2=1. We show these systems to be superintegrable of arbitrarily high order and work out explicitly the structure of the symmetry algebras determined by the 5 basis generators we have constructed. We demonstrate that the symmetry algebras close rationally; only for systems admitting extra discrete symmetries is polynomial closure achieved. Underlying the structure theory is the existence of raising and lowering constants of the motion, not themselves polynomials in the momenta, that can be employed to construct the polynomial symmetries and their structure relations.
Blocks of finite groups and their invariants
Sambale, Benjamin
2014-01-01
Providing a nearly complete selection of up-to-date methods and results on block invariants with respect to their defect groups, this book covers the classical theory pioneered by Brauer, the modern theory of fusion systems introduced by Puig, the geometry of numbers developed by Minkowski, the classification of finite simple groups, and various computer assisted methods. In a powerful combination, these tools are applied to solve many special cases of famous open conjectures in the representation theory of finite groups. Most of the material is drawn from peer-reviewed journal articles, but there are also new previously unpublished results. In order to make the text self-contained, detailed proofs are given whenever possible. Several tables add to the text's usefulness as a reference. The book is aimed at experts in group theory or representation theory who may wish to make use of the presented ideas in their research.
Pérez-Nadal, Guillem
2016-01-01
We consider a non-relativistic free scalar field theory with a type of anisotropic scale invariance in which the number of coordinates "scaling like time" is generically greater than one. We propose the Cartesian product of two curved spaces, with the metric of each space parameterized by the other space, as a notion of curved background to which the theory can be extended. We study this type of geometries, and find a family of extensions of the theory to curved backgrounds in which the anisotropic scale invariance is promoted to a local, Weyl-type symmetry.
Invariant differential operators
Dobrev, Vladimir K
2016-01-01
With applications in quantum field theory, elementary particle physics and general relativity, this two-volume work studies invariance of differential operators under Lie algebras, quantum groups, superalgebras including infinite-dimensional cases, Schrödinger algebras, applications to holography. This first volume covers the general aspects of Lie algebras and group theory.
Institute of Scientific and Technical Information of China (English)
Chen Wen-Xue; Zhang Shu-Lian; Zhang Peng; Zeng Zhao-Li
2012-01-01
In this paper,we propose a semi-classical theory to successfully explain the polarization flipping in a single frequency laser. An experimental setup is built to verify this theory. The observed experimental phenomena are consistent with the theoretical analysis.We perform phase retardation measurements of birefringent components using this experimental system.The results show that the measurement repeatability is 0.12° and the measurement accuracy is 0.22°.
Sussman, Joshua; Beaujean, A. Alexander; Worrell, Frank C.; Watson, Stevie
2013-01-01
Item response models (IRMs) were used to analyze Cross Racial Identity Scale (CRIS) scores. Rasch analysis scores were compared with classical test theory (CTT) scores. The partial credit model demonstrated a high goodness of fit and correlations between Rasch and CTT scores ranged from 0.91 to 0.99. CRIS scores are supported by both methods.…
Tapavicza, Enrico; Tavernelli, Ivano; Rothlisberger, Ursula; Filippi, Claudia; Casida, Mark E.
2008-01-01
We present a mixed time-dependent density-functional theory (TDDFT)/classical trajectory surface hopping (SH) study of the photochemical ring opening in oxirane. Previous preparatory work limited to the symmetric CC ring-opening pathways of oxirane concluded that the Tamm-Dancoff approximation (TDA)
Mason, Brandon; Smithey, Martha
2012-01-01
This study examines Merton's Classical Strain Theory (1938) as a causative factor in intimate partner violence among college students. We theorize that college students experience general life strain and cumulative strain as they pursue the goal of a college degree. We test this strain on the likelihood of using intimate partner violence. Strain…
Thermoelectric properties of fully hydrogenated graphene: Semi-classical Boltzmann theory
Energy Technology Data Exchange (ETDEWEB)
Reshak, A. H., E-mail: maalidph@yahoo.co.uk [New Technologies-Research Centre, University of West Bohemia, Univerzitni 8, 306 14 Pilsen (Czech Republic); Center of Excellence Geopolymer and Green Technology, School of Material Engineering, University Malaysia Perlis, 01007 Kangar, Perlis (Malaysia)
2015-06-14
Based on the calculated band structure, the electronic transport coefficients of chair-/boat-like graphane were evaluated by using the semi-classical Boltzmann theory and rigid band model. The maximum value of electrical conductivity for chair (boat)-like graphane of about 1.4 (0.6) × 10{sup 19} (Ωms){sup −1} is achieved at 600 K. The charge carrier concentration and the electrical conductivity linearly increase with increasing the temperature in agreement with the experimental work for graphene. The investigated materials exhibit the highest value of Seebeck coefficient at 300 K. We should emphasize that in the chemical potential between ∓0.125 μ(eV) the investigated materials exhibit minimum value of electronic thermal conductivity, therefore, maximum efficiency. As the temperature increases, the electronic thermal conductivity increases exponentially, in agreement with the experimental data of graphene. We also calculated the power factor of chair-/boat-like graphane at 300 and 600 K as a function of chemical potential between ∓0.25 μ(eV)
Polar-solvation classical density-functional theory for electrolyte aqueous solutions near a wall
Warshavsky, Vadim; Marucho, Marcelo
2016-04-01
A precise description of the structural and dielectric properties of liquid water is critical to understanding the physicochemical properties of solutes in electrolyte solutions. In this article, a mixture of ionic and dipolar hard spheres is considered to account for water crowding and polarization effects on ionic electrical double layers near a uniformly charged hard wall. As a unique feature, solvent hard spheres carrying a dipole at their centers were used to model water molecules at experimentally known concentration, molecule size, and dipolar moment. The equilibrium ionic and dipole density profiles of this electrolyte aqueous model were calculated using a polar-solvation classical density-functional theory (PSCDFT). These profiles were used to calculate the charge density distribution, water polarization, dielectric permittivity function, and mean electric potential profiles as well as differential capacitance, excess adsorptions, and wall-fluid surface tension. These results were compared with those corresponding to the pure dipolar model and unpolar primitive solvent model of electrolyte aqueous solutions to understand the role that water crowding and polarization effects play on the structural and thermodynamic properties of these systems. Overall, PSCDFT predictions are in agreement with available experimental data.
Diemand, Jürg; Angélil, Raymond; Tanaka, Kyoko K; Tanaka, Hidekazu
2014-11-01
We present results from direct, large-scale molecular dynamics simulations of homogeneous bubble (liquid-to-vapor) nucleation. The simulations contain half a billion Lennard-Jones atoms and cover up to 56 million time steps. The unprecedented size of the simulated volumes allows us to resolve the nucleation and growth of many bubbles per run in simple direct micro-canonical simulations while the ambient pressure and temperature remain almost perfectly constant. We find bubble nucleation rates which are lower than in most of the previous, smaller simulations. It is widely believed that classical nucleation theory (CNT) generally underestimates bubble nucleation rates by very large factors. However, our measured rates are within two orders of magnitude of CNT predictions; only at very low temperatures does CNT underestimate the nucleation rate significantly. Introducing a small, positive Tolman length leads to very good agreement at all temperatures, as found in our recent vapor-to-liquid nucleation simulations. The critical bubbles sizes derived with the nucleation theorem agree well with the CNT predictions at all temperatures. Local hot spots reported in the literature are not seen: Regions where a bubble nucleation event will occur are not above the average temperature, and no correlation of temperature fluctuations with subsequent bubble formation is seen.
Unification of classical nucleation theories via a unified Itô-Stratonovich stochastic equation.
Durán-Olivencia, Miguel A; Lutsko, James F
2015-09-01
Classical nucleation theory (CNT) is the most widely used framework to describe the early stage of first-order phase transitions. Unfortunately, the different points of view adopted to derive it yield different kinetic equations for the probability density function, e.g., Zeldovich-Frenkel or Becker-Döring-Tunitskii equations. Starting from a phenomenological stochastic differential equation, a unified equation is obtained in this work. In other words, CNT expressions are recovered by selecting one or another stochastic calculus. Moreover, it is shown that the unified CNT thus obtained produces the same Fokker-Planck equation as that from a recent update of CNT [J. F. Lutsko and M. A. Durán-Olivencia, J. Chem. Phys. 138, 244908 (2013)10.1063/1.4811490] when mass transport is governed by diffusion. Finally, we derive a general induction-time expression along with specific approximations of it to be used under different scenarios, in particular, when the mass-transport mechanism is governed by direct impingement, volume diffusion, surface diffusion, or interface transfer.
Gong, Kai; Marshall, Bennett D; Chapman, Walter G
2013-09-07
We study the lower critical solution temperature (LCST) behavior of associating polymer brushes (i.e., poly(N-isopropylacrylamide)) using classical density functional theory. Without using any empirical or temperature-dependent parameters, we find the phase transition of polymer brushes from extended to collapsed structure with increasing temperature, indicating the LCST behavior of polymer brushes. The LCST behavior of associating polymer brushes is attributed to the interplay of hydrogen bonding interactions and Lennard-Jones attractions in the system. The effect of grafting density and molecular weight on the phase behavior of associating polymer brushes has been also investigated. We find no LCST behavior at low grafting density or molecular weight. Moreover, increasing grafting density decreases the LCST and swelling ratio of polymer brushes. Similarly, increasing molecular weight decreases the LCST but increases the swelling ratio. At very high grafting density, a partial collapsed structure appears near the LCST. Qualitatively consistent with experiments, our results provide insight into the molecular mechanism of LCST behavior of associating polymer brushes.
Fan, Peifeng; Liu, Jian; Xiang, Nong; Yu, Zhi
2016-01-01
A manifestly covariant, or geometric, field theory for relativistic classical particle-field system is developed. The connection between space-time symmetry and energy-momentum conservation laws for the system is established geometrically without splitting the space and time coordinates, i.e., space-time is treated as one identity without choosing a coordinate system. To achieve this goal, we need to overcome two difficulties. The first difficulty arises from the fact that particles and field reside on different manifold. As a result, the geometric Lagrangian density of the system is a function of the 4-potential of electromagnetic fields and also a functional of particles' world-lines. The other difficulty associated with the geometric setting is due to the mass-shell condition. The standard Euler-Lagrange (EL) equation for a particle is generalized into the geometric EL equation when the mass-shell condition is imposed. For the particle-field system, the geometric EL equation is further generalized into a w...
Directory of Open Access Journals (Sweden)
Igor V. Uporov
2015-09-01
Full Text Available The dipole interaction model is a classical electromagnetic theory for calculating circular dichroism (CD resulting from the π-π* transitions of amides. The theoretical model, pioneered by J. Applequist, is assembled into a package, DInaMo, written in Fortran allowing for treatment of proteins. DInaMo reads Protein Data Bank formatted files of structures generated by molecular mechanics or reconstructed secondary structures. Crystal structures cannot be used directly with DInaMo; they either need to be rebuilt with idealized bond angles and lengths, or they need to be energy minimized to adjust bond lengths and bond angles because it is common for crystal structure geometries to have slightly short bond lengths, and DInaMo is sensitive to this. DInaMo reduces all the amide chromophores to points with anisotropic polarizability and all nonchromophoric aliphatic atoms including hydrogens to points with isotropic polarizability; all other atoms are ignored. By determining the interactions among the chromophoric and nonchromophoric parts of the molecule using empirically derived polarizabilities, the rotational and dipole strengths are determined leading to the calculation of CD. Furthermore, ignoring hydrogens bound to methyl groups is initially explored and proves to be a good approximation. Theoretical calculations on 24 proteins agree with experiment showing bands with similar morphology and maxima.
Decoherence and the Appearance of a Classical World in Quantum Theory
Energy Technology Data Exchange (ETDEWEB)
Alicki, R [Instytut Fizyki Teoretycznej i Astrofizyki, Uniwersytet Gdanski, ul Wita Stwosza 57, 80-952 Gdansk (Poland)
2004-02-06
decoherence in quantum information processing and even decoherence in the brain. The next chapter, written by Kiefer, is devoted to decoherence in quantum field theory and quantum gravity which is a much more speculative and less explored topic. Two complementary aspects are studied in this approach: decoherence of particle states by the quantum fields and decoherence of field states by the particles. Cosmological issues related to decoherence are discussed, not only within the standard Friedmann cosmology, but also using the elements of the theory of black holes, wormholes and strings. The relations between the formalism of consistent histories defined in terms of decoherence functionals and the environmental decoherence are discussed in chapter 5, also written by Kiefer. The Feynman--Vernon influence functional for the quantum open system is presented in detail as the first example of decoherence functional. Then the general theory is outlined together with possible interpretations including cosmological aspects. The next chapter by Giulini presents an overview of the superselection rules arising from physical symmetries and gauge transformations both for nonrelativistic quantum mechanics and quantum field theory. Critical discussion of kinematical superselection rules versus dynamical ones is illustrated by numerous examples like Galilei invariant quantum mechanics, quantum electrodynamics and quantum gravity. The introduction to the theory of quantum open systems and its applications to decoherence models is given in chapter 7 by Kupsch. Generalized master equations, Markovian approximation and a few Hamiltonian models relevant for decoherence are discussed. Some mathematical tools, e.g., complete positivity and entropy inequalities are also presented. The last chapter by Stamatescu is devoted to stochastic collapse models which can be interpreted either as certain representations of the dynamics of open quantum systems or as fundamental modifications of the Schroedinger
BOOK REVIEW: Decoherence and the Appearance of a Classical World in Quantum Theory
Alicki, R.
2004-02-01
decoherence in quantum information processing and even decoherence in the brain. The next chapter, written by Kiefer, is devoted to decoherence in quantum field theory and quantum gravity which is a much more speculative and less explored topic. Two complementary aspects are studied in this approach: decoherence of particle states by the quantum fields and decoherence of field states by the particles. Cosmological issues related to decoherence are discussed, not only within the standard Friedmann cosmology, but also using the elements of the theory of black holes, wormholes and strings. The relations between the formalism of consistent histories defined in terms of decoherence functionals and the environmental decoherence are discussed in chapter 5, also written by Kiefer. The Feynman--Vernon influence functional for the quantum open system is presented in detail as the first example of decoherence functional. Then the general theory is outlined together with possible interpretations including cosmological aspects. The next chapter by Giulini presents an overview of the superselection rules arising from physical symmetries and gauge transformations both for nonrelativistic quantum mechanics and quantum field theory. Critical discussion of kinematical superselection rules versus dynamical ones is illustrated by numerous examples like Galilei invariant quantum mechanics, quantum electrodynamics and quantum gravity. The introduction to the theory of quantum open systems and its applications to decoherence models is given in chapter 7 by Kupsch. Generalized master equations, Markovian approximation and a few Hamiltonian models relevant for decoherence are discussed. Some mathematical tools, e.g., complete positivity and entropy inequalities are also presented. The last chapter by Stamatescu is devoted to stochastic collapse models which can be interpreted either as certain representations of the dynamics of open quantum systems or as fundamental modifications of the Schr
Lorentz-invariant formulation of Cherenkov radiation by tachyons
Jones, F. C.
1972-01-01
Previous treatments of Cherenkov radiation, electromagnetic and gravitational, by tachyons were in error because the prescription employed to cut off the divergent integral over frequency is not a Lorentz invariant procedure. The resulting equation of motion for the tachyon is therefore not covariant. The proper procedure requires an extended, deformable distribution of charge or mass and yields a particularly simple form for the tachyon's world line, one that could be deduced from simple invariance considerations. It is shown that Cherenkov radiation by tachyons implys their ultimate annihilation with an antitachyon and demonstrates a disturbing property of tachyons, namely the impossibility of specifying arbitrary Cauchy data even in a purely classical theory.
Lorentz invariant relative velocity and relativistic binary collisions
Cannoni, Mirco
2017-01-01
This paper reviews the concept of Lorentz invariant relative velocity that is often misunderstood or unknown in high energy physics literature. The properties of the relative velocity allow to formulate the invariant flux and cross-section without recurring to nonphysical velocities or any assumption about the reference frame. Applications such as the luminosity of a collider, the use as kinematic variable, and the statistical theory of collisions in a relativistic classical gas are reviewed. It is emphasized how the hyperbolic properties of the velocity space explain the peculiarities of relativistic scattering.
Lorentz invariant relative velocity and relativistic binary collisions
Cannoni, Mirco
2016-01-01
This article reviews the concept of Lorentz invariant relative velocity that is often misunderstood or unknown in high energy physics literature. The properties of the relative velocity allow to formulate the invariant flux and cross section without recurring to non--physical velocities or any assumption about the reference frame. Applications such as the luminosity of a collider, the use as kinematic variable, and the statistical theory of collisions in a relativistic classical gas are reviewed. It is emphasized how the hyperbolic properties of the velocity space explain the peculiarities of relativistic scattering.
Boyer, Timothy H.
2016-11-01
Electromagnetism is a relativistic theory, and one must exercise care in coupling this theory with nonrelativistic classical mechanics and with nonrelativistic classical statistical mechanics. Indeed historically, both the blackbody radiation spectrum and diamagnetism within classical theory have been misunderstood because of two crucial failures: (1) the neglect of classical electromagnetic zero-point radiation, and (2) the use of erroneous combinations of nonrelativistic mechanics with relativistic electrodynamics. Here we review the treatment of classical blackbody radiation, and show that the presence of Lorentz-invariant classical electromagnetic zero-point radiation can explain both the Planck blackbody spectrum and Landau diamagnetism at thermal equilibrium within classical electromagnetic theory. The analysis requires that relativistic electromagnetism is joined appropriately with simple nonrelativistic mechanical systems which can be regarded as the zero-velocity limits of relativistic systems, and that nonrelativistic classical statistical mechanics is applied only in the low-frequency limit when zero-point energy makes no contribution.
Lorentz invariance with an invariant energy scale
Magueijo, J; Magueijo, Joao; Smolin, Lee
2002-01-01
We propose a modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertial frames and agreement with Einstein's theory at low energies. This is accomplished by a non-linear modification of the action of the Lorentz group on momentum space, generated by adding a dilatation to each boost in such a way that the Planck energy remains invariant. The associated algebra has unmodified structure constants, and we highlight the similarities between the group action found and a transformation previously proposed by Fock. We also discuss the resulting modifications of field theory and suggest a modification of the equivalence principle which determines how the new theory is embedded in general relativity.
Weyl invariance and black hole evaporation
Navarro-Salas, J; Talavera, C F
1995-01-01
We consider the semiclassical dynamics of CGHS black holes with a Weyl-invariant effective action for conformal matter. The trace anomaly of Polyakov effective action is converted into the Virasoro anomaly thus leading to the same flux of Hawking radiation. The covariance of semiclassical equations can be restored through a non-local redefinition of the metric-dilaton fields. The resulting theory turns out to be equivalent to the RST model. This provides a mechanism to solve semiclassical equations of 2D dilaton gravity coupled to conformal matter for classically soluble models.
Cosmological disformal invariance
Domènech, Guillem; Sasaki, Misao
2015-01-01
The invariance of physical observables under disformal transformations is considered. It is known that conformal transformations leave physical observables invariant. However, whether it is true for disformal transformations is still an open question. In this paper, it is shown that a pure disformal transformation without any conformal factor is equivalent to rescaling the time coordinate. Since this rescaling applies equally to all the physical quantities, physics must be invariant under a disformal transformation, that is, neither causal structure, propagation speed nor any other property of the fields are affected by a disformal transformation itself. This fact is presented at the action level for gravitational and matter fields and it is illustrated with some examples of observable quantities. We also find the physical invariance for cosmological perturbations at linear and high orders in perturbation, extending previous studies. Finally, a comparison with Horndeski and beyond Horndeski theories under a d...
Complete Pick Positivity and Unitary Invariance
Bhattacharya, Angshuman
2009-01-01
The characteristic function for a contraction is a classical complete unitary invariant devised by Sz.-Nagy and Foias. Just as a contraction is related to the Szego kernel $k_S(z,w) = (1 - z\\ow)^{-1}$ for $|z|, |w| < 1$, by means of $(1/k_S)(T,T^*) \\ge 0$, we consider an arbitrary open connected domain $\\Omega$ in $\\BC^n$, a complete Nevanilinna-Pick kernel $k$ on $\\Omega$ and a tuple $T = (T_1, ..., T_n)$ of commuting bounded operators on a complex separable Hilbert space $\\clh$ such that $(1/k)(T,T^*) \\ge 0$. For a complete Pick kernel the $1/k$ functional calculus makes sense in a beautiful way. It turns out that the model theory works very well and a characteristic function can be associated with $T$. Moreover, the characteristic function then is a complete unitary invariant for a suitable class of tuples $T$.
Chopin, E
2000-01-01
We show how to reformulate gauge theories coupled to scalar fields in terms of explicitly gauge-invariant variables. We show in the case of scalar QED that the classical theory can be reformulated in this way. We discuss the form of some realistic asymptotic solutions of these equations. The equations of motion are then also reformulated in the non-abelian case.
Finsler-like structures from Lorentz-breaking classical particles
Russell, Neil
2015-01-01
A method is presented for deducing classical point-particle Lagrange functions corresponding to a class of quartic dispersion relations. Applying this to particles violating Lorentz symmetry in the minimal Standard-Model Extension leads to a variety of novel lagrangians in flat spacetime. Morphisms in these classical systems are studied that echo invariance under field redefinitions in the quantized theory. The Lagrange functions found offer new possibilities for understanding Lorentz-breaking effects by exploring parallels with Finsler-like geometries.
Energetics of high-speed running: integrating classical theory and contemporary observations.
Weyand, Peter G; Bundle, Matthew W
2005-04-01
We hypothesized that the anaerobic power and aerobic power outputs during all-out runs of any common duration between 10 and 150 s would be proportional to the maximum anaerobic (E(an-max)) and aerobic powers (E(aer-max)) available to the individual runner. Seventeen runners who differed in E(an-max) and E(aer-max) (5 sprinters, 5 middle-distance runners, and 7 long distance runners) were tested during treadmill running on a 4.6 degrees incline. E(an-max) was estimated from the fastest treadmill speed subjects could attain for eight steps. E(aer-max) was determined from a progressive, discontinuous, treadmill test to failure. Oxygen deficits and rates of uptake were measured to assess the respective anaerobic and aerobic power outputs during 11-16 all-out treadmill runs that elicited failure between 10 and 220 s. We found that, during all-out runs of any common duration, the relative anaerobic and aerobic powers utilized were largely the same for sprint, middle-distance, and long-distance subjects. The similar fractional utilization of the E(an-max) and E(aer-max) available during high-speed running 1) provides empirical values that modify and advance classic theory, 2) allows rates of anaerobic and aerobic energy release to be quantified from individual maxima and run durations, and 3) explains why the high-speed running performances of different event specialists can be accurately predicted (R(2) = 0.97; n = 254) from two direct measurements and the same exponential time constant.
Ickes, Luisa; Welti, André; Lohmann, Ulrike
2017-02-01
Heterogeneous ice formation by immersion freezing in mixed-phase clouds can be parameterized in general circulation models (GCMs) by classical nucleation theory (CNT). CNT parameterization schemes describe immersion freezing as a stochastic process, including the properties of insoluble aerosol particles in the droplets. There are different ways to parameterize the properties of aerosol particles (i.e., contact angle schemes), which are compiled and tested in this paper. The goal of this study is to find a parameterization scheme for GCMs to describe immersion freezing with the ability to shift and adjust the slope of the freezing curve compared to homogeneous freezing to match experimental data. We showed in a previous publication that the resulting freezing curves from CNT are very sensitive to unconstrained kinetic and thermodynamic parameters in the case of homogeneous freezing. Here we investigate how sensitive the outcome of a parameter estimation for contact angle schemes from experimental data is to unconstrained kinetic and thermodynamic parameters. We demonstrate that the parameters describing the contact angle schemes can mask the uncertainty in thermodynamic and kinetic parameters. Different CNT formulations are fitted to an extensive immersion freezing dataset consisting of size-selected measurements as a function of temperature and time for different mineral dust types, namely kaolinite, illite, montmorillonite, microcline (K-feldspar), and Arizona test dust. We investigated how accurate different CNT formulations (with estimated fit parameters for different contact angle schemes) reproduce the measured freezing data, especially the time and particle size dependence of the freezing process. The results are compared to a simplified deterministic freezing scheme. In this context, we evaluated which CNT-based parameterization scheme able to represent particle properties is the best choice to describe immersion freezing in a GCM.
Classical test theory versus Rasch analysis for quality of life questionnaire reduction
Directory of Open Access Journals (Sweden)
Lamarca Rosa
2003-07-01
Full Text Available Abstract Background Although health-related quality of life (HRQOL instruments may offer satisfactory results, their length often limits the extent to which they are actually applied in clinical practice. Efforts to develop short questionnaires have largely focused on reducing existing instruments. The approaches most frequently employed for this purpose rely on statistical procedures that are considered exponents of Classical Test Theory (CTT. Despite the popularity of CTT, two major conceptual limitations have been pointed out: the lack of an explicit ordered continuum of items that represent a unidimensional construct, and the lack of additivity of rating scale data. In contrast to the CTT approach, the Rasch model provides an alternative scaling methodology that enables the examination of the hierarchical structure, unidimensionality and additivity of HRQOL measures. METHODS: In order to empirically compare CTT and Rasch Analysis (RA results, this paper presents the parallel reduction of a 38-item questionnaire, the Nottingham Health Profile (NHP, through the analysis of the responses of a sample of 9,419 individuals. Results CTT resulted in 20 items (4 dimensions whereas RA in 22 items (2 dimensions. Both instruments showed similar characteristics under CTT requirements: item-total correlation ranged 0.45–0.75 for NHP20 and 0.46–0.68 for NHP22, while reliability ranged 0.82–0.93 and 0.87–94 respectively. Conclusions Despite the differences in content, NHP20 and NHP22 convergent scores also showed high degrees of association (0.78–0.95. Although the unidimensional view of health of the NHP20 and NHP22 composite scores was also confirmed by RA, NHP20 dimensions failed to meet the goodness-of fit criteria established by the Rasch model, precluding the interval-level of measurement of its scores.
Quantum-Classical Correspondence of Shortcuts to Adiabaticity
Okuyama, Manaka; Takahashi, Kazutaka
2017-04-01
We formulate the theory of shortcuts to adiabaticity in classical mechanics. For a reference Hamiltonian, the counterdiabatic term is constructed from the dispersionless Korteweg-de Vries (KdV) hierarchy. Then the adiabatic theorem holds exactly for an arbitrary choice of time-dependent parameters. We use the Hamilton-Jacobi theory to define the generalized action. The action is independent of the history of the parameters and is directly related to the adiabatic invariant. The dispersionless KdV hierarchy is obtained from the classical limit of the KdV hierarchy for the quantum shortcuts to adiabaticity. This correspondence suggests some relation between the quantum and classical adiabatic theorems.
Energy Technology Data Exchange (ETDEWEB)
Dartora, C.A., E-mail: cadartora@eletrica.ufpr.b [Electrical Engineering Department, Federal University of Parana (UFPR) (Brazil); Cabrera, G.G., E-mail: cabrera@ifi.unicamp.b [Instituto de Fisica ' Gleb Wataghin' , Universidade Estadual de Campinas (UNICAMP), C.P. 6165, Campinas 13.083-970 SP (Brazil)
2010-05-31
The non-relativistic Pauli-Schroedinger theory has a richer gauge structure than usually expected, being invariant under the U(1)xSU(2) gauge group, which allows to define spin-current density vectors and obtains the relevant conserved quantities from Noether's theorem. The electromagnetic fields E and B play the role of the gauge potentials for the SU(2) sector of the gauge group and can possibly contribute with a corresponding invariant curvature self-energy term in the Lagrangian density. From the dynamics of the U(1) and SU(2) gauge fields we show that electric fields can be induced by spin-currents originated from the SU(2) gauge symmetry.
Fiorentini, M A L Capri D; Mintz, B W; Palhares, L F; Sorella, S P
2016-01-01
We address the issue of the renormalizability of the gauge-invariant non-local dimension-two operator $A^2_{\\rm min}$, whose minimization is defined along the gauge orbit. Despite its non-local character, we show that the operator $A^2_{\\rm min}$ can be cast in local form through the introduction of an auxiliary Stueckelberg field. The localization procedure gives rise to an unconventional kind of Stueckelberg-type action which turns out to be renormalizable to all orders of perturbation theory. In particular, as a consequence of its gauge invariance, the anomalous dimension of the operator $A^2_{\\rm min}$ turns out to be independent from the gauge parameter $\\alpha$ entering the gauge-fixing condition, being thus given by the anomalous dimension of the operator $A^2$ in the Landau gauge.
Breaking Weyl invariance in the interior of a bubble
Energy Technology Data Exchange (ETDEWEB)
Wood, W.R.; Papini, G. (Department of Physics, University of Regina, Regina, Saskatchewan, S4S 0A2 (Canada))
1992-05-15
The basis on which Weyl's unified theory of gravitation and electromagnetism was rejected is reconsidered from a new perspective. It is argued that while Weyl's theory, as indeed any classical theory, is incapable of explaining atomic phenomena, this does not nullify the geometric interpretation of the exterior electromagnetic field; it simply reflects the fact that some form of quantization is needed to account for atomic standards of length. In support of this argument the Gauss-Mainardi-Codazzi formalism is employed to demonstrate that it is possible to construct a bubble in Weyl space where the exterior geometry is conformally invariant and the electromagnetic field can be given a geometric interpretation, while at the same time a standard of length can be introduced into the theory by breaking the conformal invariance in the interior of the bubble.
Breaking Weyl invariance in the interior of a bubble
Wood, W. R.; Papini, G.
1992-05-01
The basis on which Weyl's unified theory of gravitation and electromagnetism was rejected is reconsidered from a new perspective. It is argued that while Weyl's theory, as indeed any classical theory, is incapable of explaining atomic phenomena, this does not nullify the geometric interpretation of the exterior electromagnetic field; it simply reflects the fact that some form of quantization is needed to account for atomic standards of length. In support of this argument the Gauss-Mainardi-Codazzi formalism is employed to demonstrate that it is possible to construct a bubble in Weyl space where the exterior geometry is conformally invariant and the electromagnetic field can be given a geometric interpretation, while at the same time a standard of length can be introduced into the theory by breaking the conformal invariance in the interior of the bubble.
Two New Types of Rings Defined by Using a Translational Invariant Fuzzy Subset
Directory of Open Access Journals (Sweden)
Manal Ghanem
2010-01-01
Full Text Available We use a translational invariant fuzzy subset of a ring to define two new types of commutative rings namely, -presimplifiable and -associate rings. We present some results of these rings. The interest of these results is that most of them are mirrors of corresponding results of presimplifiable and associate rings in classical ring theory.
Quantum field theory and classical optics: determining the fine structure constant
Leuchs, Gerd; Hawton, Margaret; Sanchez-Soto, Luis L.
2016-01-01
The properties of the vacuum are described by quantum physics including the response to external fields such as electromagnetic radiation. Of the two parameters that govern the details of the electromagnetic field dynamics in vacuum, one is fixed by the requirement of Lorentz invariance $c= 1/\\sqrt{\\varepsilon_{0} \\mu_{0}}$. The other one, $Z_{0}= \\sqrt{\\mu_{0}/\\varepsilon_{0}} = 1/(c\\varepsilon_{0})$ and its relation to the quantum vacuum, is discussed in this contribution. Deriving $\\vareps...
Kaufmann, Lukas; Marcolli, Claudia; Luo, Beiping; Peter, Thomas
2017-03-01
Homogeneous nucleation of ice in supercooled water droplets is a stochastic process. In its classical description, the growth of the ice phase requires the emergence of a critical embryo from random fluctuations of water molecules between the water bulk and ice-like clusters, which is associated with overcoming an energy barrier. For heterogeneous ice nucleation on ice-nucleating surfaces both stochastic and deterministic descriptions are in use. Deterministic (singular) descriptions are often favored because the temperature dependence of ice nucleation on a substrate usually dominates the stochastic time dependence, and the ease of representation facilitates the incorporation in climate models. Conversely, classical nucleation theory (CNT) describes heterogeneous ice nucleation as a stochastic process with a reduced energy barrier for the formation of a critical embryo in the presence of an ice-nucleating surface. The energy reduction is conveniently parameterized in terms of a contact angle α between the ice phase immersed in liquid water and the heterogeneous surface. This study investigates various ice-nucleating agents in immersion mode by subjecting them to repeated freezing cycles to elucidate and discriminate the time and temperature dependences of heterogeneous ice nucleation. Freezing rates determined from such refreeze experiments are presented for Hoggar Mountain dust, birch pollen washing water, Arizona test dust (ATD), and also nonadecanol coatings. For the analysis of the experimental data with CNT, we assumed the same active site to be always responsible for freezing. Three different CNT-based parameterizations were used to describe rate coefficients for heterogeneous ice nucleation as a function of temperature, all leading to very similar results: for Hoggar Mountain dust, ATD, and larger nonadecanol-coated water droplets, the experimentally determined increase in freezing rate with decreasing temperature is too shallow to be described properly by
Open and Closed String field theory interpreted in classical Algebraic Topology
Sullivan, Dennis
2003-01-01
There is an interpretation of open string field theory in algebraic topology. An interpretation of closed string field theory can be deduced from this open string theory to obtain as well the interpretation of open and closed string field theory combined.
Kerner, Boris S
2016-01-01
We show that the minimization of travel times in a network as generally accepted in classical traffic and transportation theories deteriorates the traffic system through a considerable increase in the probability of traffic breakdown in the network. We introduce a network characteristic {\\it minimum network capacity} that shows that rather than the minimization of travel times in the network, the minimization of the probability of traffic breakdown in the network maximizes the network throughput at which free flow persists in the whole network.
Classical nucleation theory of homogeneous freezing of water: thermodynamic and kinetic parameters.
Ickes, Luisa; Welti, André; Hoose, Corinna; Lohmann, Ulrike
2015-02-28
The probability of homogeneous ice nucleation under a set of ambient conditions can be described by nucleation rates using the theoretical framework of Classical Nucleation Theory (CNT). This framework consists of kinetic and thermodynamic parameters, of which three are not well-defined (namely the interfacial tension between ice and water, the activation energy and the prefactor), so that any CNT-based parameterization of homogeneous ice formation is less well-constrained than desired for modeling applications. Different approaches to estimate the thermodynamic and kinetic parameters of CNT are reviewed in this paper and the sensitivity of the calculated nucleation rate to the choice of parameters is investigated. We show that nucleation rates are very sensitive to this choice. The sensitivity is governed by one parameter - the interfacial tension between ice and water, which determines the energetic barrier of the nucleation process. The calculated nucleation rate can differ by more than 25 orders of magnitude depending on the choice of parameterization for this parameter. The second most important parameter is the activation energy of the nucleation process. It can lead to a variation of 16 orders of magnitude. By estimating the nucleation rate from a collection of droplet freezing experiments from the literature, the dependence of these two parameters on temperature is narrowed down. It can be seen that the temperature behavior of these two parameters assumed in the literature does not match with the predicted nucleation rates from the fit in most cases. Moreover a comparison of all possible combinations of theoretical parameterizations of the dominant two free parameters shows that one combination fits the fitted nucleation rates best, which is a description of the interfacial tension coming from a molecular model [Reinhardt and Doye, J. Chem. Phys., 2013, 139, 096102] in combination with the activation energy derived from self-diffusion measurements [Zobrist
Quantum and classical behavior in interacting bosonic systems
Energy Technology Data Exchange (ETDEWEB)
Hertzberg, Mark P. [Institute of Cosmology & Department of Physics and Astronomy, Tufts University,Medford, MA 02155 (United States)
2016-11-21
It is understood that in free bosonic theories, the classical field theory accurately describes the full quantum theory when the occupancy numbers of systems are very large. However, the situation is less understood in interacting theories, especially on time scales longer than the dynamical relaxation time. Recently there have been claims that the quantum theory deviates spectacularly from the classical theory on this time scale, even if the occupancy numbers are extremely large. Furthermore, it is claimed that the quantum theory quickly thermalizes while the classical theory does not. The evidence for these claims comes from noticing a spectacular difference in the time evolution of expectation values of quantum operators compared to the classical micro-state evolution. If true, this would have dramatic consequences for many important phenomena, including laboratory studies of interacting BECs, dark matter axions, preheating after inflation, etc. In this work we critically examine these claims. We show that in fact the classical theory can describe the quantum behavior in the high occupancy regime, even when interactions are large. The connection is that the expectation values of quantum operators in a single quantum micro-state are approximated by a corresponding classical ensemble average over many classical micro-states. Furthermore, by the ergodic theorem, a classical ensemble average of local fields with statistical translation invariance is the spatial average of a single micro-state. So the correlation functions of the quantum and classical field theories of a single micro-state approximately agree at high occupancy, even in interacting systems. Furthermore, both quantum and classical field theories can thermalize, when appropriate coarse graining is introduced, with the classical case requiring a cutoff on low occupancy UV modes. We discuss applications of our results.
A New Semi-Symmetric Uniﬁed Field Theory of the Classical Fields of Gravity and Electromagnetism
Directory of Open Access Journals (Sweden)
Suhendro I.
2007-10-01
Full Text Available We attempt to present a classical theoretical framework in which the gravitational and electromagnetic fields are unified as intrinsic geometric objects in the space-time manifold. For this purpose, we first present the preliminary geometric considerations dealing with the metric differential geometry of Cartan connections. The unified field theory is then developed as an extension of the general theory of relativity based on a semi- symmetric Cartan connection which is meant to be as close as possible structurally to the symmetric connection of the Einstein-Riemann space-time.
Nakamura, Kouji
2010-01-01
We derived the second-order perturbations of the Einstein equations and the Klein-Gordon equation for a generic situation in terms of gauge-invariant variables. The consistency of all the equations is confirmed. This confirmation implies that all the derived equations of the second order are self-consistent and these equations are correct in this sense. We also discuss the physical implication of these equations.