Form factor of relativistic two-particle system and covariant hamiltonian formulation of quantum field theory

International Nuclear Information System (INIS)

Skachkov, N.; Solovtsov, I.

1979-01-01

Based on the hamiltonian formulation of quantum field theory proposed by Kadyshevsky the three-dimensional relativistic approach is developed for describing the form factors of composite systems. The main features of the diagram technique appearing in the covariant hamiltonian formulation of field theory are discussed. The three-dimensional relativistic equation for the vertex function is derived and its connection with that for the quasipotential wave function is found. The expressions are obtained for the form factor of the system through equal-time two-particle wave functions both in momentum and relativistic configurational representations. An explicit expression for the form factor is found for the case of two-particle interaction through the Coulomb potential

Hamiltonian mechanics and divergence-free fields

International Nuclear Information System (INIS)

Boozer, A.H.

1986-08-01

The field lines, or integral curves, of a divergence-free field in three dimensions are shown to be topologically equivalent to the trajectories of a Hamiltonian with two degrees of freedom. The consideration of fields that depend on a parameter allow the construction of a canonical perturbation theory which is valid even if the perturbation is large. If the parametric dependence of the magnetic, or the vorticity field is interpreted as time dependence, evolution equations are obtained which give Kelvin's theorem or the flux conservation theorem for ideal fluids and plasmas. The Hamiltonian methods prove especially useful for study of fields in which the field lines must be known throughout a volume of space

Strong coupling expansion for scattering phases in hamiltonian lattice field theories. Pt. 1. The (d+1)-dimensional Ising model

International Nuclear Information System (INIS)

Dahmen, Bernd

1994-01-01

A systematic method to obtain strong coupling expansions for scattering quantities in hamiltonian lattice field theories is presented. I develop the conceptual ideas for the case of the hamiltonian field theory analogue of the Ising model, in d space and one time dimension. The main result is a convergent series representation for the scattering states and the transition matrix. To be explicit, the special cases of d=1 and d=3 spatial dimensions are discussed in detail. I compute the next-to-leading order approximation for the phase shifts. The application of the method to investigate low-energy scattering phenomena in lattice gauge theory and QCD is proposed. ((orig.))

The Hamiltonian formulation of regular rth-order Lagrangian field theories

International Nuclear Information System (INIS)

Shadwick, W.F.

1982-01-01

A Hamiltonian formulation of regular rth-order Lagrangian field theories over an m-dimensional manifold is presented in terms of the Hamilton-Cartan formalism. It is demonstrated that a uniquely determined Cartan m-form may be associated to an rth-order Lagrangian by imposing conditions of congruence modulo a suitably defined system of contact m-forms. A geometric regularity condition is given and it is shown that, for a regular Lagrangian, the momenta defined by the Hamilton-Cartan formalism, together with the coordinates on the (r-1)st-order jet bundle, are a minimal set of local coordinates needed to express the Euler-Lagrange equations. When r is greater than one, the number of variables required is strictly less than the dimension of the (2r-1)st order jet bundle. It is shown that, in these coordinates, the Euler-Lagrange equations take the first-order Hamiltonian form given by de Donder. It is also shown that the geometrically natural generalization of the Hamilton-Jacobi procedure for finding extremals is equivalent to de Donder's Hamilton-Jacobi equation. (orig.)

Scattering theory of infrared divergent Pauli-Fierz Hamiltonians

CERN Document Server

Derezinski, J

2003-01-01

We consider in this paper the scattering theory of infrared divergent massless Pauli-Fierz Hamiltonians. We show that the CCR representations obtained from the asymptotic field contain so-called {\\em coherent sectors} describing an infinite number of asymptotically free bosons. We formulate some conjectures leading to mathematically well defined notion of {\\em inclusive and non-inclusive scattering cross-sections} for Pauli-Fierz Hamiltonians. Finally we give a general description of the scattering theory of QFT models in the presence of coherent sectors for the asymptotic CCR representations.

Geometric Hamiltonian structures and perturbation theory

International Nuclear Information System (INIS)

Omohundro, S.

1984-08-01

We have been engaged in a program of investigating the Hamiltonian structure of the various perturbation theories used in practice. We describe the geometry of a Hamiltonian structure for non-singular perturbation theory applied to Hamiltonian systems on symplectic manifolds and the connection with singular perturbation techniques based on the method of averaging

Hamiltonian truncation approach to quenches in the Ising field theory

Directory of Open Access Journals (Sweden)

T. Rakovszky

2016-10-01

Full Text Available In contrast to lattice systems where powerful numerical techniques such as matrix product state based methods are available to study the non-equilibrium dynamics, the non-equilibrium behaviour of continuum systems is much harder to simulate. We demonstrate here that Hamiltonian truncation methods can be efficiently applied to this problem, by studying the quantum quench dynamics of the 1+1 dimensional Ising field theory using a truncated free fermionic space approach. After benchmarking the method with integrable quenches corresponding to changing the mass in a free Majorana fermion field theory, we study the effect of an integrability breaking perturbation by the longitudinal magnetic field. In both the ferromagnetic and paramagnetic phases of the model we find persistent oscillations with frequencies set by the low-lying particle excitations not only for small, but even for moderate size quenches. In the ferromagnetic phase these particles are the various non-perturbative confined bound states of the domain wall excitations, while in the paramagnetic phase the single magnon excitation governs the dynamics, allowing us to capture the time evolution of the magnetisation using a combination of known results from perturbation theory and form factor based methods. We point out that the dominance of low lying excitations allows for the numerical or experimental determination of the mass spectra through the study of the quench dynamics.

Gauge theories of infinite dimensional Hamiltonian superalgebras

International Nuclear Information System (INIS)

Sezgin, E.

1989-05-01

Symplectic diffeomorphisms of a class of supermanifolds and the associated infinite dimensional Hamiltonian superalgebras, H(2M,N) are discussed. Applications to strings, membranes and higher spin field theories are considered: The embedding of the Ramond superconformal algebra in H(2,1) is obtained. The Chern-Simons gauge theory of symplectic super-diffeomorphisms is constructed. (author). 29 refs

Scattering theory for Stark Hamiltonians

International Nuclear Information System (INIS)

Jensen, Arne

1994-01-01

An introduction to the spectral and scattering theory for Schroedinger operators is given. An abstract short range scattering theory is developed. It is applied to perturbations of the Laplacian. Particular attention is paid to the study of Stark Hamiltonians. The main result is an explanation of the discrepancy between the classical and the quantum scattering theory for one-dimensional Stark Hamiltonians. (author). 47 refs

Magnetic field line Hamiltonian

International Nuclear Information System (INIS)

Boozer, A.H.

1984-03-01

The magnetic field line Hamiltonian and the associated canonical form for the magnetic field are important concepts both for understanding toroidal plasma physics and for practical calculations. A number of important properties of the canonical or Hamiltonian representation are derived and their importance is explained

Covariant description of Hamiltonian form for field dynamics

International Nuclear Information System (INIS)

Ozaki, Hiroshi

2005-01-01

Hamiltonian form of field dynamics is developed on a space-like hypersurface in space-time. A covariant Poisson bracket on the space-like hypersurface is defined and it plays a key role to describe every algebraic relation into a covariant form. It is shown that the Poisson bracket has the same symplectic structure that was brought in the covariant symplectic approach. An identity invariant under the canonical transformations is obtained. The identity follows a canonical equation in which the interaction Hamiltonian density generates a deformation of the space-like hypersurface. The equation just corresponds to the Yang-Feldman equation in the Heisenberg pictures in quantum field theory. By converting the covariant Poisson bracket on the space-like hypersurface to four-dimensional commutator, we can pass over to quantum field theory in the Heisenberg picture without spoiling the explicit relativistic covariance. As an example the canonical QCD is displayed in a covariant way on a space-like hypersurface

Contribution from the interaction Hamiltonian to the expectation value of particle number with the non-equilibrium quantum field theory

International Nuclear Information System (INIS)

Hotta, Ryuuichi; Morozumi, Takuya; Takata, Hiroyuki

2012-01-01

We develop the method analyzing particle number non-conserving phenomena with non-equilibrium quantum field-theory. In this study, we consider a CP violating model with interaction Hamiltonian that breaks particle number conservation. To derive the quantum Boltzmann equation for the particle number, we solve Schwinger-Dyson equation, which are obtained from two particle irreducible closed-time-path (2PI CTP) effective action. In this calculation, we show the contribution from interaction Hamiltonian to the time evolution of expectation value of particle number.

Hamiltonian approach to GR. Pt. 2. Covariant theory of quantum gravity

Energy Technology Data Exchange (ETDEWEB)

Cremaschini, Claudio [Faculty of Philosophy and Science, Silesian University in Opava, Institute of Physics and Research Center for Theoretical Physics and Astrophysics, Opava (Czech Republic); Tessarotto, Massimo [University of Trieste, Department of Mathematics and Geosciences, Trieste (Italy); Faculty of Philosophy and Science, Silesian University in Opava, Institute of Physics, Opava (Czech Republic)

2017-05-15

A non-perturbative quantum field theory of General Relativity is presented which leads to a new realization of the theory of covariant quantum gravity (CQG-theory). The treatment is founded on the recently identified Hamiltonian structure associated with the classical space-time, i.e., the corresponding manifestly covariant Hamilton equations and the related Hamilton-Jacobi theory. The quantum Hamiltonian operator and the CQG-wave equation for the corresponding CQG-state and wave function are realized in 4-scalar form. The new quantum wave equation is shown to be equivalent to a set of quantum hydrodynamic equations which warrant the consistency with the classical GR Hamilton-Jacobi equation in the semiclassical limit. A perturbative approximation scheme is developed, which permits the adoption of the harmonic oscillator approximation for the treatment of the Hamiltonian potential. As an application of the theory, the stationary vacuum CQG-wave equation is studied, yielding a stationary equation for the CQG-state in terms of the 4-scalar invariant-energy eigenvalue associated with the corresponding approximate quantum Hamiltonian operator. The conditions for the existence of a discrete invariant-energy spectrum are pointed out. This yields a possible estimate for the graviton mass together with a new interpretation about the quantum origin of the cosmological constant. (orig.)

Strong coupling expansion for scattering phases in hamiltonian lattice field theories. Pt. 2. SU(2) gauge theory in (2+1) dimensions

International Nuclear Information System (INIS)

Dahmen, B.

1994-12-01

A recently proposed method for a strong coupling analysis of scattering phenomena in hamiltonian lattice field theories is applied to the SU(2) Yang-Mills model in (2 + 1) dimensions. The calculation is performed up to second order in the hopping parameter. All relevant quantities that characterize the collision between the lightest glueballs in the elastic region - cross section, phase shifts, resonance parameters - are determined. (orig.)

Faddeev-Jackiw Hamiltonian reduction for free and gauged Rarita-Schwinger theories

Energy Technology Data Exchange (ETDEWEB)

Dengiz, Suat [Massachusetts Institute of Technology, Center for Theoretical Physics, Cambridge, MA (United States)

2016-10-15

We study the Faddeev-Jackiw symplectic Hamiltonian reduction for 3 + 1-dimensional free and Abelian gauged Rarita-Schwinger theories that comprise Grassmannian fermionic fields. We obtain the relevant fundamental brackets and find that they are in convenient forms for quantization. The brackets are independent of whether the theories contain mass or gauge fields, and the structures of constraints and symplectic potentials largely determine characteristic behaviors of the theories. We also note that, in contrast to the free massive theory, the Dirac field equations for free massless Rarita-Schwinger theory cannot be obtained in a covariant way. (orig.)

Finite-size scaling theory and quantum hamiltonian Field theory: the transverse Ising model

International Nuclear Information System (INIS)

Hamer, C.J.; Barber, M.N.

1979-01-01

Exact results for the mass gap, specific heat and susceptibility of the one-dimensional transverse Ising model on a finite lattice are generated by constructing a finite matrix representation of the Hamiltonian using strong-coupling eigenstates. The critical behaviour of the limiting infinite chain is analysed using finite-size scaling theory. In this way, excellent estimates (to within 1/2% accuracy) are found for the critical coupling and the exponents α, ν and γ

Covariant Noncommutative Field Theory

Energy Technology Data Exchange (ETDEWEB)

Estrada-Jimenez, S [Licenciaturas en Fisica y en Matematicas, Facultad de Ingenieria, Universidad Autonoma de Chiapas Calle 4a Ote. Nte. 1428, Tuxtla Gutierrez, Chiapas (Mexico); Garcia-Compean, H [Departamento de Fisica, Centro de Investigacion y de Estudios Avanzados del IPN P.O. Box 14-740, 07000 Mexico D.F., Mexico and Centro de Investigacion y de Estudios Avanzados del IPN, Unidad Monterrey Via del Conocimiento 201, Parque de Investigacion e Innovacion Tecnologica (PIIT) Autopista nueva al Aeropuerto km 9.5, Lote 1, Manzana 29, cp. 66600 Apodaca Nuevo Leon (Mexico); Obregon, O [Instituto de Fisica de la Universidad de Guanajuato P.O. Box E-143, 37150 Leon Gto. (Mexico); Ramirez, C [Facultad de Ciencias Fisico Matematicas, Universidad Autonoma de Puebla, P.O. Box 1364, 72000 Puebla (Mexico)

2008-07-02

The covariant approach to noncommutative field and gauge theories is revisited. In the process the formalism is applied to field theories invariant under diffeomorphisms. Local differentiable forms are defined in this context. The lagrangian and hamiltonian formalism is consistently introduced.

Covariant Noncommutative Field Theory

International Nuclear Information System (INIS)

Estrada-Jimenez, S.; Garcia-Compean, H.; Obregon, O.; Ramirez, C.

2008-01-01

The covariant approach to noncommutative field and gauge theories is revisited. In the process the formalism is applied to field theories invariant under diffeomorphisms. Local differentiable forms are defined in this context. The lagrangian and hamiltonian formalism is consistently introduced

Hamiltonian representation of divergence-free fields

International Nuclear Information System (INIS)

Boozer, A.H.

1984-11-01

Globally divergence-free fields, such as the magnetic field and the vorticity, can be described by a two degree of freedom Hamiltonian. The Hamiltonian function provides a complete topological description of the field lines. The formulation also separates the dissipative and inertial time scale evolution of the magnetic and the vorticity fields

Treatment of the intrinsic Hamiltonian in particle-number nonconserving theories

International Nuclear Information System (INIS)

Hergert, H.; Roth, R.

2009-01-01

We discuss the implications of using an intrinsic Hamiltonian in theories without particle-number conservation, e.g., the Hartree-Fock-Bogoliubov approximation, where the Hamiltonian's particle-number dependence leads to discrepancies if one naively replaces the particle-number operator by its expectation value. We develop a systematic expansion that fixes this problem and leads to an a posteriori justification of the widely-used one- plus two-body form of the intrinsic kinetic energy in nuclear self-consistent field methods. The expansion's convergence properties as well as its practical applications are discussed for several sample nuclei.

Hamiltonian description of toroidal magnetic fields in vacuum

International Nuclear Information System (INIS)

Lewis, H.R.; Bates, J.W.

1996-01-01

An investigation of vacuum magnetic fields in toroidal geometry has been initiated. Previously, the general form of the magnetic scalar potential for fields regular at the poloidal axis was given. Here, these results have been expanded to obtain the magnetic scalar potential in a vacuum region that may surround a toroidal current distribution. Using this generalized magnetic scalar potential in conjunction with Boozer's canonical representation of a magnetic field, a field-line Hamiltonian for nonaxisymmetric vacuum fields has been derived. These fields axe being examined using a novel, open-quotes time-dependentclose quotes perturbation theory, which permits the iterative construction of invariants associated with magnetic field-line Hamiltonians that consist of an axisymmetric zeroth-order term, plus a nonaxisymmetric perturbation. By choosing appropriate independent variables, an explicit constructive procedure is developed which involves only a single canonical transformation. Such invariants are of interest because they provide a means of investigating the topology of magnetic field lines. Our objective is to elucidate the existence of magnetic surfaces for nonaxisymmetric vacuum configurations, as well as to provide an approach for studying the onset of stochastic behavior

Significance of constraints associated with Green's functions in Hamiltonian perturbation theory

International Nuclear Information System (INIS)

Maharana, L.; Muller-Kirsten, H.J.W.; Wiedemann, A.

1987-01-01

In many formulations of Hamiltonian perturbation theory a Green's function becomes undefined when some parameter is allowed to vanish. Here various examples are discussed to illustrate this phenomenon, and it is shown that they are all realizations of a general theorem. The cases considered are examples in classical mechanics, quantum mechanics, electrodynamics and field theory. The prime object is to illustrate the unity of the examples and thus to make the application of the procedure to field theory models of current interest more transparent. One example that it is referred to is the skyrmion model

EMR-related problems at the interface between the crystal field Hamiltonians and the zero-field splitting Hamiltonians

Directory of Open Access Journals (Sweden)

Rudowicz Czesław

2015-07-01

Full Text Available The interface between optical spectroscopy, electron magnetic resonance (EMR, and magnetism of transition ions forms the intricate web of interrelated notions. Major notions are the physical Hamiltonians, which include the crystal field (CF (or equivalently ligand field (LF Hamiltonians, and the effective spin Hamiltonians (SH, which include the zero-field splitting (ZFS Hamiltonians as well as to a certain extent also the notion of magnetic anisotropy (MA. Survey of recent literature has revealed that this interface, denoted CF (LF ↔ SH (ZFS, has become dangerously entangled over the years. The same notion is referred to by three names that are not synonymous: CF (LF, SH (ZFS, and MA. In view of the strong need for systematization of nomenclature aimed at bringing order to the multitude of different Hamiltonians and the associated quantities, we have embarked on this systematization. In this article, we do an overview of our efforts aimed at providing a deeper understanding of the major intricacies occurring at the CF (LF ↔ SH (ZFS interface with the focus on the EMR-related problems for transition ions.

Bell-type quantum field theories

International Nuclear Information System (INIS)

Duerr, Detlef; Goldstein, Sheldon; Tumulka, Roderich; Zanghi, Nino

2005-01-01

In his paper (1986 Beables for quantum field theory Phys. Rep. 137 49-54) John S Bell proposed how to associate particle trajectories with a lattice quantum field theory, yielding what can be regarded as a vertical bar Ψ vertical bar 2 -distributed Markov process on the appropriate configuration space. A similar process can be defined in the continuum, for more or less any regularized quantum field theory; we call such processes Bell-type quantum field theories. We describe methods for explicitly constructing these processes. These concern, in addition to the definition of the Markov processes, the efficient calculation of jump rates, how to obtain the process from the processes corresponding to the free and interaction Hamiltonian alone, and how to obtain the free process from the free Hamiltonian or, alternatively, from the one-particle process by a construction analogous to 'second quantization'. As an example, we consider the process for a second quantized Dirac field in an external electromagnetic field. (topical review)

Magnetic charge in an octonionic field theory

International Nuclear Information System (INIS)

Lassig, C.C.; Jashi, G.C.

1996-01-01

The violation of the Jacobi identity by the presence of magnetic charge is accommodated by using an explicitly nonassociative theory of octonionic fields. Lagrangian and Hamiltonian formalisms are constructed, and issues of the quantisation discussed. Finally an extension of these concepts to string theory is contemplated. The two main problems that seems to arise in this octonionic field theory are the difficulty of constructing an appropriate action to suit the desired equations of motion, and the failure to complete a Hamiltonian formalism and hence quantize the theory. 8 refs

BRST quantization of Yang-Mills theory: A purely Hamiltonian approach on Fock space

Science.gov (United States)

Öttinger, Hans Christian

2018-04-01

We develop the basic ideas and equations for the BRST quantization of Yang-Mills theories in an explicit Hamiltonian approach, without any reference to the Lagrangian approach at any stage of the development. We present a new representation of ghost fields that combines desirable self-adjointness properties with canonical anticommutation relations for ghost creation and annihilation operators, thus enabling us to characterize the physical states on a well-defined Fock space. The Hamiltonian is constructed by piecing together simple BRST invariant operators to obtain a minimal invariant extension of the free theory. It is verified that the evolution equations implied by the resulting minimal Hamiltonian provide a quantum version of the classical Yang-Mills equations. The modifications and requirements for the inclusion of matter are discussed in detail.

Lie transforms and their use in Hamiltonian perturbation theory

International Nuclear Information System (INIS)

Cary, J.R.

1978-06-01

A review is presented of the theory of Lie transforms as applied to Hamiltonian systems. We begin by presenting some general background on the Hamiltonian formalism and by introducing the operator notation for canonical transformations. We then derive the general theory of Lie transforms. We derive the formula for the new Hamiltonian when one uses a Lie transform to effect a canonical transformation, and we use Lie transforms to prove a very general version of Noether's theorem, or the symmetry-equals-invariant theorem. Next we use the general Lie transform theory to derive Deprit's perturbation theory. We illustrate this perturbation theory by application to two well-known problems in classical mechanics. Finally we present a chapter on conventions. There are many ways to develop Lie transforms. The last chapter explains the reasons for the choices made here

Residual gauge invariance of Hamiltonian lattice gauge theories

International Nuclear Information System (INIS)

Ryang, S.; Saito, T.; Shigemoto, K.

1984-01-01

The time-independent residual gauge invariance of Hamiltonian lattice gauge theories is considered. Eigenvalues and eigenfunctions of the unperturbed Hamiltonian are found in terms of Gegengauer's polynomials. Physical states which satisfy the subsidiary condition corresponding to Gauss' law are constructed systematically. (orig.)

Equivalence of ADM Hamiltonian and Effective Field Theory approaches at next-to-next-to-leading order spin1-spin2 coupling of binary inspirals

Energy Technology Data Exchange (ETDEWEB)

Levi, Michele [Institut d' Astrophysique de Paris, Université Pierre et Marie Curie, CNRS-UMR 7095, 98 bis Boulevard Arago, 75014 Paris (France); Steinhoff, Jan, E-mail: michele.levi@upmc.fr, E-mail: jan.steinhoff@ist.utl.pt [Centro Multidisciplinar de Astrofisica, Instituto Superior Tecnico, Universidade de Lisboa, Avenida Rovisco Pais 1, 1049-001 Lisboa (Portugal)

2014-12-01

The next-to-next-to-leading order spin1-spin2 potential for an inspiralling binary, that is essential for accuracy to fourth post-Newtonian order, if both components in the binary are spinning rapidly, has been recently derived independently via the ADM Hamiltonian and the Effective Field Theory approaches, using different gauges and variables. Here we show the complete physical equivalence of the two results, thereby we first prove the equivalence of the ADM Hamiltonian and the Effective Field Theory approaches at next-to-next-to-leading order with the inclusion of spins. The main difficulty in the spinning sectors, which also prescribes the manner in which the comparison of the two results is tackled here, is the existence of redundant unphysical spin degrees of freedom, associated with the spin gauge choice of a point within the extended spinning object for its representative worldline. After gauge fixing and eliminating the unphysical degrees of freedom of the spin and its conjugate at the level of the action, we arrive at curved spacetime generalizations of the Newton-Wigner variables in closed form, which can also be used to obtain further Hamiltonians, based on an Effective Field Theory formulation and computation. Finally, we make use of our validated result to provide gauge invariant relations among the binding energy, angular momentum, and orbital frequency of an inspiralling binary with generic compact spinning components to fourth post-Newtonian order, including all known sectors up to date.

Effective Hamiltonian theory: recent formal results and non-nuclear applications

International Nuclear Information System (INIS)

Brandow, B.H.

1981-01-01

Effective Hamiltonian theory is discussed from the points of view of the unitary transformation method and degenerate perturbation theory. It is shown that the two approaches are identical term by term. The main features of a formulation of the coupled-cluster method for open-shell systems are outlined. Finally, recent applications of the many-body linked-cluster form of degenerate perturbation theory are described: the derivation of effective spin Hamiltonians in magnetic insulator systems, the derivation and calculation ab initio of effective π-electron Hamiltonians for planar conjugated hydrocarbon molecules, and understanding the so-called valence fluctuation phenomenon exhibited by certain rare earth compounds

Light-front quantization of field theory

Energy Technology Data Exchange (ETDEWEB)

Srivastava, Prem P. [Universidade do Estado, Rio de Janeiro, RJ (Brazil). Inst. de Fisica]|[Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)

1996-07-01

Some basic topics in Light-Front (LF) quantized field theory are reviewed. Poincare algebra and the LF spin operator are discussed. The local scalar field theory of the conventional framework is shown to correspond to a non-local Hamiltonian theory on the LF in view of the constraint equations on the phase space, which relate the bosonic condensates to the non-zero modes. This new ingredient is useful to describe the spontaneous symmetry breaking on the LF. The instability of the symmetric phase in two dimensional scalar theory when the coupling constant grows is shown in the LF theory renormalized to one loop order. Chern-Simons gauge theory, regarded to describe excitations with fractional statistics, is quantized in the light-cone gauge and a simple LF Hamiltonian obtained which may allow us to construct renormalized theory of anyons. (author). 20 refs.

Light-front quantization of field theory

International Nuclear Information System (INIS)

Srivastava, Prem P.

1996-07-01

Some basic topics in Light-Front (LF) quantized field theory are reviewed. Poincare algebra and the LF spin operator are discussed. The local scalar field theory of the conventional framework is shown to correspond to a non-local Hamiltonian theory on the LF in view of the constraint equations on the phase space, which relate the bosonic condensates to the non-zero modes. This new ingredient is useful to describe the spontaneous symmetry breaking on the LF. The instability of the symmetric phase in two dimensional scalar theory when the coupling constant grows is shown in the LF theory renormalized to one loop order. Chern-Simons gauge theory, regarded to describe excitations with fractional statistics, is quantized in the light-cone gauge and a simple LF Hamiltonian obtained which may allow us to construct renormalized theory of anyons. (author). 20 refs

Renormalization of Hamiltonians

International Nuclear Information System (INIS)

Glazek, S.D.; Wilson, K.G.

1993-01-01

This paper presents a new renormalization procedure for Hamiltonians such as those of light-front field theory. The bare Hamiltonian with an arbitrarily large, but finite cutoff, is transformed by a specially chosen similarity transformation. The similarity transformation has two desirable features. First, the transformed Hamiltonian is band diagonal: in particular, all matrix elements vanish which would otherwise have caused transitions with big energy jumps, such as from a state of bounded energy to a state with an energy of the order of the cutoff. At the same time, neither the similarity transformation nor the transformed Hamiltonian, computed in perturbation theory, contain vanishing or near-vanishing energy denominators. Instead, energy differences in denominators can be replaced by energy sums for purposes of order of magnitude estimates needed to determine cutoff dependences. These two properties make it possible to determine relatively easily the list of counterterms needed to obtain finite low energy results (such as for eigenvalues). A simple model Hamiltonian is discussed to illustrate the method

Combining symmetry collective states with coupled-cluster theory: Lessons from the Agassi model Hamiltonian

Science.gov (United States)

Hermes, Matthew R.; Dukelsky, Jorge; Scuseria, Gustavo E.

2017-06-01

The failures of single-reference coupled-cluster theory for strongly correlated many-body systems is flagged at the mean-field level by the spontaneous breaking of one or more physical symmetries of the Hamiltonian. Restoring the symmetry of the mean-field determinant by projection reveals that coupled-cluster theory fails because it factorizes high-order excitation amplitudes incorrectly. However, symmetry-projected mean-field wave functions do not account sufficiently for dynamic (or weak) correlation. Here we pursue a merger of symmetry projection and coupled-cluster theory, following previous work along these lines that utilized the simple Lipkin model system as a test bed [J. Chem. Phys. 146, 054110 (2017), 10.1063/1.4974989]. We generalize the concept of a symmetry-projected mean-field wave function to the concept of a symmetry projected state, in which the factorization of high-order excitation amplitudes in terms of low-order ones is guided by symmetry projection and is not exponential, and combine them with coupled-cluster theory in order to model the ground state of the Agassi Hamiltonian. This model has two separate channels of correlation and two separate physical symmetries which are broken under strong correlation. We show how the combination of symmetry collective states and coupled-cluster theory is effective in obtaining correlation energies and order parameters of the Agassi model throughout its phase diagram.

Perturbation theory of effective Hamiltonians

International Nuclear Information System (INIS)

Brandow, B.H.

1975-01-01

This paper constitutes a review of the many papers which have used perturbation theory to derive ''effective'' or ''model'' Hamiltonians. It begins with a brief review of nondegenerate and non-many-body perturbation theory, and then considers the degenerate but non-many-body problem in some detail. It turns out that the degenerate perturbation problem is not uniquely defined, but there are some practical criteria for choosing among the various possibilities. Finally, the literature dealing with the linked-cluster aspects of open-shell many-body systems is reviewed. (U.S.)

Effective field theory for triaxially deformed nuclei

Energy Technology Data Exchange (ETDEWEB)

Chen, Q.B. [Technische Universitaet Muechen, Physik-Department, Garching (Germany); Peking University, State Key Laboratory of Nuclear Physics and Technology, School of Physics, Beijing (China); Kaiser, N. [Technische Universitaet Muechen, Physik-Department, Garching (Germany); Meissner, Ulf G. [Universitaet Bonn, Helmholtz-Institut fuer Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Bonn (Germany); Institute for Advanced Simulation, Institut fuer Kernphysik, Juelich Center for Hadron Physics and JARA-HPC, Forschungszentrum Juelich, Juelich (Germany); Meng, J. [Peking University, State Key Laboratory of Nuclear Physics and Technology, School of Physics, Beijing (China); Beihang University, School of Physics and Nuclear Energy Engineering, Beijing (China); University of Stellenbosch, Department of Physics, Stellenbosch (South Africa)

2017-10-15

Effective field theory is generalized to investigate the rotational motion of triaxially deformed even-even nuclei. The Hamiltonian for the triaxial rotor is obtained up to next-to-leading order within the effective field theory formalism. Its applicability is examined by comparing with a five-dimensional rotor-vibrator Hamiltonian for the description of the energy spectra of the ground state and γ band in Ru isotopes. It is found that by taking into account the next-to-leading order corrections, the ground state band in the whole spin region and the γ band in the low spin region are well described. The deviations for high-spin states in the γ bands point towards the importance of including vibrational degrees of freedom in the effective field theory formulation. (orig.)

k-Cosymplectic Classical Field Theories: Tulczyjew and Skinner-Rusk Formulations

Science.gov (United States)

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.

k-Cosymplectic Classical Field Theories: Tulczyjew and Skinner–Rusk Formulations

International Nuclear Information System (INIS)

Rey, Angel M.; Román-Roy, Narciso; Salgado, Modesto; Vilariño, Silvia

2012-01-01

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.

A Hamiltonian functional for the linearized Einstein vacuum field equations

International Nuclear Information System (INIS)

Rosas-RodrIguez, R

2005-01-01

By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a conserved functional as Hamiltonian; this Hamiltonian is not the analog of the energy of the field. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained. The generator of spatial translations associated with such bracket is also obtained

Hamiltonian theory of wave and particle in quantum mechanics 2. Hamilton-Jacobi theory and particle back-reaction

International Nuclear Information System (INIS)

Holland, P.

2001-01-01

Pursuing the Hamiltonian formulation of the De Broglie-Bohm (deBB) theory presented in the preceding paper, the Hamilton-Jacobi (HJ) theory of the wave-particle system is developed. It is shown how to derive a HJ equation for the particle, which enables trajectories to be computed algebraically using Jacobi's method. Using Liouville's equation in the HJ representation it was found the restriction on the Jacobi solutions which implies the quantal distribution. This gives a first method for interpreting the deBB theory in HJ terms. A second method proceeds via an explicit solution of the field+particle HJ equation. Both methods imply that the quantum phase may be interpreted as an incomplete integral. Using these results and those of the first paper it is shown how Schroedinger's equation can be represented in Liouvilian terms, and vice versa. The general theory of canonical transformations that represent quantum unitary transformations is given, and it is shown in principle how the trajectory theory may be expressed in other quantum representations. Using the solution found for the total HJ equation, an explicit solution for the additional field containing a term representing the particle back-reaction is found. The conservation of energy and momentum in the model is established, and weak form of the action-reaction principle is shown to hold. Alternative forms for the Hamiltonian are explored and it is shown that, within this theoretical context, the deBB theory is not unique. The theory potentially provides an alternative way of obtaining the classical limit

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...... by the physically relevant choices. The translation invariance implies that the Hamiltonian may be decomposed into a direct integral over the space of total momentum where the fixed momentum fiber Hamiltonians are given by , where denotes total momentum and is the Segal field operator. The fiber Hamiltonians...

Hamiltonian analysis of Plebanski theory

International Nuclear Information System (INIS)

Buffenoir, E; Henneaux, M; Noui, K; Roche, Ph

2004-01-01

We study the Hamiltonian formulation of Plebanski theory in both the Euclidean and Lorentzian cases. A careful analysis of the constraints shows that the system is non-regular, i.e., the rank of the Dirac matrix is non-constant on the non-reduced phase space. We identify the gravitational and topological sectors which are regular subspaces of the non-reduced phase space. The theory can be restricted to the regular subspace which contains the gravitational sector. We explicitly identify first- and second-class constraints in this case. We compute the determinant of the Dirac matrix and the natural measure for the path integral of the Plebanski theory (restricted to the gravitational sector). This measure is the analogue of the Leutwyler-Fradkin-Vilkovisky measure of quantum gravity

Local algebras in Euclidean quantum field theory

International Nuclear Information System (INIS)

Guerra, Francesco.

1975-06-01

The general structure of the local observable algebras of Euclidean quantum field theory is described, considering the very simple examples of the free scalar field, the vector meson field, and the electromagnetic field. The role of Markov properties, and the relations between Euclidean theory and Hamiltonian theory in Minkowski space-time are especially emphasized. No conflict appears between covariance (in the Euclidean sense) and locality (in the Markov sense) on one hand and positive definiteness of the metric on the other hand [fr

Hamiltonian lattice field theory: Computer calculations using variational methods

International Nuclear Information System (INIS)

Zako, R.L.

1991-01-01

I develop a variational method for systematic numerical computation of physical quantities -- bound state energies and scattering amplitudes -- in quantum field theory. An infinite-volume, continuum theory is approximated by a theory on a finite spatial lattice, which is amenable to numerical computation. I present an algorithm for computing approximate energy eigenvalues and eigenstates in the lattice theory and for bounding the resulting errors. I also show how to select basis states and choose variational parameters in order to minimize errors. The algorithm is based on the Rayleigh-Ritz principle and Kato's generalizations of Temple's formula. The algorithm could be adapted to systems such as atoms and molecules. I show how to compute Green's functions from energy eigenvalues and eigenstates in the lattice theory, and relate these to physical (renormalized) coupling constants, bound state energies and Green's functions. Thus one can compute approximate physical quantities in a lattice theory that approximates a quantum field theory with specified physical coupling constants. I discuss the errors in both approximations. In principle, the errors can be made arbitrarily small by increasing the size of the lattice, decreasing the lattice spacing and computing sufficiently long. Unfortunately, I do not understand the infinite-volume and continuum limits well enough to quantify errors due to the lattice approximation. Thus the method is currently incomplete. I apply the method to real scalar field theories using a Fock basis of free particle states. All needed quantities can be calculated efficiently with this basis. The generalization to more complicated theories is straightforward. I describe a computer implementation of the method and present numerical results for simple quantum mechanical systems

Hamiltonian lattice field theory: Computer calculations using variational methods

International Nuclear Information System (INIS)

Zako, R.L.

1991-01-01

A variational method is developed for systematic numerical computation of physical quantities-bound state energies and scattering amplitudes-in quantum field theory. An infinite-volume, continuum theory is approximated by a theory on a finite spatial lattice, which is amenable to numerical computation. An algorithm is presented for computing approximate energy eigenvalues and eigenstates in the lattice theory and for bounding the resulting errors. It is shown how to select basis states and choose variational parameters in order to minimize errors. The algorithm is based on the Rayleigh-Ritz principle and Kato's generalizations of Temple's formula. The algorithm could be adapted to systems such as atoms and molecules. It is shown how to compute Green's functions from energy eigenvalues and eigenstates in the lattice theory, and relate these to physical (renormalized) coupling constants, bound state energies and Green's functions. Thus one can compute approximate physical quantities in a lattice theory that approximates a quantum field theory with specified physical coupling constants. The author discusses the errors in both approximations. In principle, the errors can be made arbitrarily small by increasing the size of the lattice, decreasing the lattice spacing and computing sufficiently long. Unfortunately, the author does not understand the infinite-volume and continuum limits well enough to quantify errors due to the lattice approximation. Thus the method is currently incomplete. The method is applied to real scalar field theories using a Fock basis of free particle states. All needed quantities can be calculated efficiently with this basis. The generalization to more complicated theories is straightforward. The author describes a computer implementation of the method and present numerical results for simple quantum mechanical systems

Multi-Hamiltonian formulations and stability of higher-derivative extensions of 3d Chern-Simons

Energy Technology Data Exchange (ETDEWEB)

Abakumova, V.A.; Kaparulin, D.S.; Lyakhovich, S.L. [Tomsk State University, Physics Faculty, Tomsk (Russian Federation)

2018-02-15

Most general third-order 3d linear gauge vector field theory is considered. The field equations involve, besides the mass, two dimensionless constant parameters. The theory admits two-parameter series of conserved tensors with the canonical energy-momentum being a particular representative of the series. For a certain range of the model parameters, the series of conserved tensors include bounded quantities. This makes the dynamics classically stable, though the canonical energy is unbounded in all the instances. The free third-order equations are shown to admit constrained multi-Hamiltonian form with the 00-components of conserved tensors playing the roles of corresponding Hamiltonians. The series of Hamiltonians includes the canonical Ostrogradski's one, which is unbounded. The Hamiltonian formulations with different Hamiltonians are not connected by canonical transformations. This means, the theory admits inequivalent quantizations at the free level. Covariant interactions are included with spinor fields such that the higher-derivative dynamics remains stable at interacting level if the bounded conserved quantity exists in the free theory. In the first-order formalism, the interacting theory remains Hamiltonian and therefore it admits quantization, though the vertices are not necessarily Lagrangian in the third-order field equations. (orig.)

Hamiltonian quantization of self-dual tensor fields and a bosonic Nielsen-Ninomiya theorem

International Nuclear Information System (INIS)

Tang Waikeung

1989-01-01

The quantization of self-dual tensor fields is carried out following the procedure of Batalin and Fradkin. The (anti) self-duality constraints (either fermionic or bosonic) in the action leads to the gravitational anomaly. In the process of gauge fixing, the impossibility of the co-existence of a positive hamiltonian and covariant action is shown. A version of the Nielsen-Ninomiya theorem applies to self-dual tensor fields viz. the lattice version of the theory shows species doubling with zero net chirality. (orig.)

Equivalence of Lagrangian and Hamiltonian BRST quantizations

International Nuclear Information System (INIS)

Grigoryan, G.V.; Grigoryan, R.P.; Tyutin, I.V.

1992-01-01

Two approaches to the quantization of gauge theories using BRST symmetry are widely used nowadays: the Lagrangian quantization, developed in (BV-quantization) and Hamiltonian quantization, formulated in (BFV-quantization). For all known examples of field theory (Yang-Mills theory, gravitation etc.) both schemes give equivalent results. However the equivalence of these approaches in general wasn't proved. The main obstacle in comparing of these formulations consists in the fact, that in Hamiltonian approach the number of ghost fields is equal to the number of all first-class constraints, while in the Lagrangian approach the number of ghosts is equal to the number of independent gauge symmetries, which is equal to the number of primary first-class constraints only. This paper is devoted to the proof of the equivalence of Lagrangian and Hamiltonian quantizations for the systems with first-class constraints only. This is achieved by a choice of special gauge in the Hamiltonian approach. It's shown, that after integration over redundant variables on the functional integral we come to effective action which is constructed according to rules for construction of the effective action in Lagrangian quantization scheme

Hamiltonian approach to GR - Part 1: covariant theory of classical gravity

Science.gov (United States)

Cremaschini, Claudio; Tessarotto, Massimo

2017-05-01

A challenging issue in General Relativity concerns the determination of the manifestly covariant continuum Hamiltonian structure underlying the Einstein field equations and the related formulation of the corresponding covariant Hamilton-Jacobi theory. The task is achieved by adopting a synchronous variational principle requiring distinction between the prescribed deterministic metric tensor \\widehat{g}(r)≡ { \\widehat{g}_{μ ν }(r)} solution of the Einstein field equations which determines the geometry of the background space-time and suitable variational fields x≡ { g,π } obeying an appropriate set of continuum Hamilton equations, referred to here as GR-Hamilton equations. It is shown that a prerequisite for reaching such a goal is that of casting the same equations in evolutionary form by means of a Lagrangian parametrization for a suitably reduced canonical state. As a result, the corresponding Hamilton-Jacobi theory is established in manifestly covariant form. Physical implications of the theory are discussed. These include the investigation of the structural stability of the GR-Hamilton equations with respect to vacuum solutions of the Einstein equations, assuming that wave-like perturbations are governed by the canonical evolution equations.

Hamiltonian approach to GR. Pt. 1. Covariant theory of classical gravity

Energy Technology Data Exchange (ETDEWEB)

Cremaschini, Claudio [Silesian University in Opava, Faculty of Philosophy and Science, Institute of Physics and Research Center for Theoretical Physics and Astrophysics, Opava (Czech Republic); Tessarotto, Massimo [University of Trieste, Department of Mathematics and Geosciences, Trieste (Italy); Silesian University in Opava, Faculty of Philosophy and Science, Institute of Physics, Opava (Czech Republic)

2017-05-15

A challenging issue in General Relativity concerns the determination of the manifestly covariant continuum Hamiltonian structure underlying the Einstein field equations and the related formulation of the corresponding covariant Hamilton-Jacobi theory. The task is achieved by adopting a synchronous variational principle requiring distinction between the prescribed deterministic metric tensor g(r) ≡ {g_μ_ν(r)} solution of the Einstein field equations which determines the geometry of the background space-time and suitable variational fields x ≡ {g,π} obeying an appropriate set of continuum Hamilton equations, referred to here as GR-Hamilton equations. It is shown that a prerequisite for reaching such a goal is that of casting the same equations in evolutionary form by means of a Lagrangian parametrization for a suitably reduced canonical state. As a result, the corresponding Hamilton-Jacobi theory is established in manifestly covariant form. Physical implications of the theory are discussed. These include the investigation of the structural stability of the GR-Hamilton equations with respect to vacuum solutions of the Einstein equations, assuming that wave-like perturbations are governed by the canonical evolution equations. (orig.)

Conformal field theory and 2D critical phenomena. Part 1

International Nuclear Information System (INIS)

Zamolodchikov, A.B.; Zamolodchikov, Al.B.

1989-01-01

Review of the recent developments in the two-dimensional conformal field theory and especially its applications to the physics of 2D critical phenomena is given. It includes the Ising model, the Potts model. Minimal models, corresponding to theories invariant under higher symmetries, such as superconformal theories, parafermionic theories and theories with current and W-algebras are also discussed. Non-hamiltonian approach to two-dimensional field theory is formulated. 126 refs

Lattice field theories: non-perturbative methods of analysis

International Nuclear Information System (INIS)

Weinstein, M.

1978-01-01

A lecture is given on the possible extraction of interesting physical information from quantum field theories by studying their semiclassical versions. From the beginning the problem of solving for the spectrum states of any given continuum quantum field theory is considered as a giant Schroedinger problem, and then some nonperturbative methods for diagonalizing the Hamiltonian of the theory are explained without recourse to semiclassical approximations. The notion of a lattice appears as an artifice to handle the problems associated with the familiar infrared and ultraviolet divergences of continuum quantum field theory and in fact for all but gauge theories. 18 references

On spin chains and field theories

International Nuclear Information System (INIS)

Roiban, Radu

2004-01-01

We point out that the existence of global symmetries in a field theory is not an essential ingredient in its relation with an integrable model. We describe an obvious construction which, given an integrable spin chain, yields a field theory whose 1-loop scale transformations are generated by the spin chain hamiltonian. We also identify a necessary condition for a given field theory to be related to an integrable spin chain. As an example, we describe an anisotropic and parity-breaking generalization of the XXZ Heisenberg spin chain and its associated field theory. The system has no nonabelian global symmetries and generally does not admit a supersymmetric extension without the introduction of more propagating bosonic fields. For the case of a 2-state chain we find the spectrum and the eigenstates. For certain values of its coupling constants the field theory associated to this general type of chain is the bosonic sector of the q-deformation of N = 4 SYM theory. (author)

Spontaneous symmetry breaking of (1+1)-dimensional φ4 theory in light-front field theory. II

International Nuclear Information System (INIS)

Pinsky, S.S.; van de Sande, B.

1994-01-01

We discuss spontaneous symmetry breaking of (1+1)-dimensional φ 4 theory in light-front field theory using a Tamm-Dancoff truncation. We show that, even though light-front field theory has a simple vacuum state which is an eigenstate of the full Hamiltonian, the field can develop a nonzero vacuum expectation value. This occurs because the zero mode of the field must satisfy an operator-valued constraint equation. In the context of (1+1)-dimensional φ 4 theory we present solutions to the constraint equation using a Tamm-Dancoff truncation to a finite number of particles and modes. We study the behavior of the zero mode as a function of coupling and Fock space truncation. The zero mode introduces new interactions into the Hamiltonian which breaks the Z 2 symmetry of the theory when the coupling is stronger than the critical coupling. We investigate the energy spectrum in the symmetric and broken phases, show that the theory does not break down in the vicinity of the critical coupling, and discuss the connection to perturbation theory. Finally, we study the spectrum of the field φ and show that, in the broken phase, the field is localized away from φ=0 as one would expect from equal-time calculations. We explicitly show that tunneling occurs

A covariant canonical description of Liouville field theory

International Nuclear Information System (INIS)

Papadopoulos, G.; Spence, B.

1993-03-01

This paper presents a new parametrisation of the space of solutions of Liouville field theory on a cylinder. In this parametrisation, the solutions are well-defined and manifestly real functions over all space-time and all of parameter space. It is shown that the resulting covariant phase space of the Liouville theory is diffeomorphic to the Hamiltonian one, and to the space of initial data of the theory. The Poisson brackets are derived and shown to be those of the co-tangent bundle of the loop group of the real line. Using Hamiltonian reduction, it is shown that this covariant phase space formulation of Liouville theory may also be obtained from the covariant phase space formulation of the Wess-Zumino-Witten model. 19 refs

Nilpotent BRST charge without auxillary B fields in quantum gauge theories

International Nuclear Information System (INIS)

Tsai, E.C.

1991-01-01

This paper introduces a modified BRST transformation for non-Abelian gauge theories. In this transformation, there is no need to introduce auxiliary B fields, yet the generatior Q for the modified transformation is nilpotent and commutes with the Hamiltonian. The Lagrangian is no longer invariant under Q, but the quantum theory which is defined by the Hamiltonian is still symmetric with respect to the transformation generated by Q

Hamiltonian kinetic theory of plasma ponderomotive processes

International Nuclear Information System (INIS)

McDonald, S.W.; Kaufman, A.N.

1981-12-01

The nonlinear nonresonant interaction of plasma waves and particles is formulated in a Hamiltonian kinetic theory which treats the wave-action and particle distributions on an equal footing, thereby displaying reciprocity relations. In the quasistatic limit, a nonlinear wave-kinetic equation is obtained. The generality of the formalism allows for applications to arbitrary geometry, with the nonlinear effects expressed in terms of the linear susceptibility

Hamiltonian kinetic theory of plasma ponderomotive processes

International Nuclear Information System (INIS)

McDonald, S.W.; Kaufman, A.N.

1982-01-01

The nonlinear nonresonant interaction of plasma waves and particles is formulated in Hamiltonian kinetic theory which treats the wave-action and particle distributions on an equal footing, thereby displaying reciprocity relations. In the quasistatic limit, a nonlinear wave-kinetic equation is obtained. The generality of the formalism allows for applications to arbitrary geometry, with the nonlinear effects expressed in terms of the linear susceptibility

Theory of collective Hamiltonian

Energy Technology Data Exchange (ETDEWEB)

Zhang Qingying

1982-02-01

Starting from the cranking model, we derive the nuclear collective Hamiltonian. We expand the total energy of the collective motion of the ground state of even--even nuclei in powers of the deformation parameter ..beta... In the first approximation, we only take the lowest-order non-vanished terms in the expansion. The collective Hamiltonian thus obtained rather differs from the A. Bohr's Hamiltonian obtained by the irrotational incompressible liquid drop model. If we neglect the coupling term between ..beta..-and ..gamma..-vibration, our Hamiltonian then has the same form as that of A. Bohr. But there is a difference between these collective parameters. Our collective parameters are determined by the state of motion of the nucleous in the nuclei. They are the microscopic expressions. On the contrary, A. Bohr's collective parameters are only the simple functions of the microscopic physical quantities (such as nuclear radius and surface tension, etc.), and independent of the state of motion of the nucleons in the nuclei. Furthermore, there exist the coupling term between ..beta..-and ..gamma..-vibration and the higher-order terms in our expansion. They can be treated as the perturbations. There are no such terms in A. Bohr's Hamiltonian. These perturbation terms will influence the rotational, vibrational spectra and the ..gamma..-transition process, etc.

Construction of alternative Hamiltonian structures for field equations

Energy Technology Data Exchange (ETDEWEB)

Herrera, Mauricio [Departamento de Fisica, Facultad de Ciencias Fisicas y Matematicas, Universidad de Chile, Santiago (Chile); Hojman, Sergio A. [Departamento de Fisica, Facultad de Ciencias, Universidad de Chile, Santiago (Chile); Facultad de Educacion, Universidad Nacional Andres Bello, Santiago (Chile); Centro de Recursos Educativos Avanzados, CREA, Santiago (Chile)

2001-08-10

We use symmetry vectors of nonlinear field equations to build alternative Hamiltonian structures. We construct such structures even for equations which are usually believed to be non-Hamiltonian such as heat, Burger and potential Burger equations. We improve on a previous version of the approach using recursion operators to increase the rank of the Poisson bracket matrices. Cole-Hopf and Miura-type transformations allow the mapping of these structures from one equation to another. (author)

Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian

Energy Technology Data Exchange (ETDEWEB)

Wahlen-Strothman, J. M. [Rice Univ., Houston, TX (United States); Henderson, T. H. [Rice Univ., Houston, TX (United States); Hermes, M. R. [Rice Univ., Houston, TX (United States); Degroote, M. [Rice Univ., Houston, TX (United States); Qiu, Y. [Rice Univ., Houston, TX (United States); Zhao, J. [Rice Univ., Houston, TX (United States); Dukelsky, J. [Consejo Superior de Investigaciones Cientificas (CSIC), Madrid (Spain). Inst. de Estructura de la Materia; Scuseria, G. E. [Rice Univ., Houston, TX (United States)

2018-01-03

Coupled cluster and symmetry projected Hartree-Fock are two central paradigms in electronic structure theory. However, they are very different. Single reference coupled cluster is highly successful for treating weakly correlated systems, but fails under strong correlation unless one sacrifices good quantum numbers and works with broken-symmetry wave functions, which is unphysical for finite systems. Symmetry projection is effective for the treatment of strong correlation at the mean-field level through multireference non-orthogonal configuration interaction wavefunctions, but unlike coupled cluster, it is neither size extensive nor ideal for treating dynamic correlation. We here examine different scenarios for merging these two dissimilar theories. We carry out this exercise over the integrable Lipkin model Hamiltonian, which despite its simplicity, encompasses non-trivial physics for degenerate systems and can be solved via diagonalization for a very large number of particles. We show how symmetry projection and coupled cluster doubles individually fail in different correlation limits, whereas models that merge these two theories are highly successful over the entire phase diagram. Despite the simplicity of the Lipkin Hamiltonian, the lessons learned in this work will be useful for building an ab initio symmetry projected coupled cluster theory that we expect to be accurate in the weakly and strongly correlated limits, as well as the recoupling regime.

Ostrogradski Hamiltonian approach for geodetic brane gravity

International Nuclear Information System (INIS)

Cordero, Ruben; Molgado, Alberto; Rojas, Efrain

2010-01-01

We present an alternative Hamiltonian description of a branelike universe immersed in a flat background spacetime. This model is named geodetic brane gravity. We set up the Regge-Teitelboim model to describe our Universe where such field theory is originally thought as a second order derivative theory. We refer to an Ostrogradski Hamiltonian formalism to prepare the system to its quantization. This approach comprize the manage of both first- and second-class constraints and the counting of degrees of freedom follows accordingly.

A Monte Carlo procedure for Hamiltonians with small nonlocal correction terms

International Nuclear Information System (INIS)

Mack, G.; Pinn, K.

1986-03-01

We consider lattice field theories whose Hamiltonians contain small nonlocal correction terms. We propose to do simulations for an auxiliarly polymer system with field dependent activities. If a nonlocal correction term to the Hamiltonian is small, it need to be evaluated only rarely. (orig.)

Extended BRST symmetries in the gauge field theory

International Nuclear Information System (INIS)

Babalean, Aurel; Constantinescu, Radu; Ionescu, Carmen

2001-01-01

The BRST procedure provides one of the most powerful methods for the quantum description of the gauge field theories. As already stated, the unphysical degrees of freedom that appear in this case can be easily canceled by the introduction of the ghost type variables. In the Hamiltonian formalism, the structure of the ghost that must be used mainly depends on two factors: - the type of the theory, that this the relations among the constraints of the theory; - the extension of the symmetry to be implemented. The paper presents the structure of the extended phase space suitable for the BRST canonical quantization of a 1- reducible gauge theory in the frame of a BRST symmetry of order three. The corresponding BRST charges and the extended Hamiltonian are also constructed. (authors)

Local modular Hamiltonians from the quantum null energy condition

Science.gov (United States)

Koeller, Jason; Leichenauer, Stefan; Levine, Adam; Shahbazi-Moghaddam, Arvin

2018-03-01

The vacuum modular Hamiltonian K of the Rindler wedge in any relativistic quantum field theory is given by the boost generator. Here we investigate the modular Hamiltonian for more general half-spaces which are bounded by an arbitrary smooth cut of a null plane. We derive a formula for the second derivative of the modular Hamiltonian with respect to the coordinates of the cut which schematically reads K''=Tv v . This formula can be integrated twice to obtain a simple expression for the modular Hamiltonian. The result naturally generalizes the standard expression for the Rindler modular Hamiltonian to this larger class of regions. Our primary assumptions are the quantum null energy condition—an inequality between the second derivative of the von Neumann entropy of a region and the stress tensor—and its saturation in the vacuum for these regions. We discuss the validity of these assumptions in free theories and holographic theories to all orders in 1 /N .

Jacobi fields of completely integrable Hamiltonian systems

International Nuclear Information System (INIS)

Giachetta, G.; Mangiarotti, L.; Sardanashvily, G.

2003-01-01

We show that Jacobi fields of a completely integrable Hamiltonian system of m degrees of freedom make up an extended completely integrable system of 2m degrees of freedom, where m additional first integrals characterize a relative motion

Hamiltonian theory of guiding-center motion

Energy Technology Data Exchange (ETDEWEB)

Littlejohn, R.G.

1980-05-01

A Hamiltonian treatment of the guiding center problem is given which employs noncanonical coordinates in phase space. Separation of the unperturbed system from the perturbation is achieved by using a coordinate transformation suggested by a theorem of Darboux. As a model to illustrate the method, motion in the magnetic field B=B(x,y)z is studied. Lie transforms are used to carry out the perturbation expansion.

Hamiltonian theory of guiding-center motion

International Nuclear Information System (INIS)

Littlejohn, R.G.

1980-05-01

A Hamiltonian treatment of the guiding center problem is given which employs noncanonical coordinates in phase space. Separation of the unperturbed system from the perturbation is achieved by using a coordinate transformation suggested by a theorem of Darboux. As a model to illustrate the method, motion in the magnetic field B=B(x,y)z is studied. Lie transforms are used to carry out the perturbation expansion

First principles of Hamiltonian medicine.

Science.gov (United States)

Crespi, Bernard; Foster, Kevin; Úbeda, Francisco

2014-05-19

We introduce the field of Hamiltonian medicine, which centres on the roles of genetic relatedness in human health and disease. Hamiltonian medicine represents the application of basic social-evolution theory, for interactions involving kinship, to core issues in medicine such as pathogens, cancer, optimal growth and mental illness. It encompasses three domains, which involve conflict and cooperation between: (i) microbes or cancer cells, within humans, (ii) genes expressed in humans, (iii) human individuals. A set of six core principles, based on these domains and their interfaces, serves to conceptually organize the field, and contextualize illustrative examples. The primary usefulness of Hamiltonian medicine is that, like Darwinian medicine more generally, it provides novel insights into what data will be productive to collect, to address important clinical and public health problems. Our synthesis of this nascent field is intended predominantly for evolutionary and behavioural biologists who aspire to address questions directly relevant to human health and disease.

Hamiltonian thermodynamics of charged three-dimensional dilatonic black holes

International Nuclear Information System (INIS)

Dias, Goncalo A. S.; Lemos, Jose P. S.

2008-01-01

The action for a class of three-dimensional dilaton-gravity theories, with an electromagnetic Maxwell field and a cosmological constant, can be recast in a Brans-Dicke-Maxwell type action, with its free ω parameter. For a negative cosmological constant, these theories have static, electrically charged, and spherically symmetric black hole solutions. Those theories with well formulated asymptotics are studied through a Hamiltonian formalism, and their thermodynamical properties are found out. The theories studied are general relativity (ω→±∞), a dimensionally reduced cylindrical four-dimensional general relativity theory (ω=0), and a theory representing a class of theories (ω=-3), all with a Maxwell term. The Hamiltonian formalism is set up in three dimensions through foliations on the right region of the Carter-Penrose diagram, with the bifurcation 1-sphere as the left boundary, and anti-de Sitter infinity as the right boundary. The metric functions on the foliated hypersurfaces and the radial component of the vector potential one-form are the canonical coordinates. The Hamiltonian action is written, the Hamiltonian being a sum of constraints. One finds a new action which yields an unconstrained theory with two pairs of canonical coordinates (M,P M ;Q,P Q ), where M is the mass parameter, which for ω M is the conjugate momenta of M, Q is the charge parameter, and P Q is its conjugate momentum. The resulting Hamiltonian is a sum of boundary terms only. A quantization of the theory is performed. The Schroedinger evolution operator is constructed, the trace is taken, and the partition function of the grand canonical ensemble is obtained, where the chemical potential is the scalar electric field φ. Like the uncharged cases studied previously, the charged black hole entropies differ, in general, from the usual quarter of the horizon area due to the dilaton.

Quantum control mechanism analysis through field based Hamiltonian encoding

International Nuclear Information System (INIS)

Mitra, Abhra; Rabitz, Herschel

2006-01-01

Optimal control of quantum dynamics in the laboratory is proving to be increasingly successful. The control fields can be complex, and the mechanisms by which they operate have often remained obscure. Hamiltonian encoding (HE) has been proposed as a method for understanding mechanisms in quantum dynamics. In this context mechanism is defined in terms of the dominant quantum pathways leading to the final state of the controlled system. HE operates by encoding a special modulation into the Hamiltonian and decoding its signature in the dynamics to determine the dominant pathway amplitudes. Earlier work encoded the modulation directly into the Hamiltonian operators. This present work introduces the alternative scheme of field based HE, where the modulation is encoded into the control field and not directly into the Hamiltonian operators. This distinct form of modulation yields a new perspective on mechanism and is computationally faster than the earlier approach. Field based encoding is also an important step towards a laboratory based algorithm for HE as it is the only form of encoding that may be experimentally executed. HE is also extended to cover systems with noise and uncertainty and finally, a hierarchical algorithm is introduced to reveal mechanism in a stepwise fashion of ever increasing detail as desired. This new hierarchical algorithm is an improvement over earlier approaches to HE where the entire mechanism was determined in one stroke. The improvement comes from the use of less complex modulation schemes, which leads to fewer evaluations of Schroedinger's equation. A number of simulations are presented on simple systems to illustrate the new field based encoding technique for mechanism assessment

Periodic solutions of asymptotically linear Hamiltonian systems without twist conditions

Energy Technology Data Exchange (ETDEWEB)

Cheng Rong [Coll. of Mathematics and Physics, Nanjing Univ. of Information Science and Tech., Nanjing (China); Dept. of Mathematics, Southeast Univ., Nanjing (China); Zhang Dongfeng [Dept. of Mathematics, Southeast Univ., Nanjing (China)

2010-05-15

In dynamical system theory, especially in many fields of applications from mechanics, Hamiltonian systems play an important role, since many related equations in mechanics can be written in an Hamiltonian form. In this paper, we study the existence of periodic solutions for a class of Hamiltonian systems. By applying the Galerkin approximation method together with a result of critical point theory, we establish the existence of periodic solutions of asymptotically linear Hamiltonian systems without twist conditions. Twist conditions play crucial roles in the study of periodic solutions for asymptotically linear Hamiltonian systems. The lack of twist conditions brings some difficulty to the study. To the authors' knowledge, very little is known about the case, where twist conditions do not hold. (orig.)

Hamiltonian approach to 1 + 1 dimensional Yang-Mills theory in Coulomb gauge

International Nuclear Information System (INIS)

Reinhardt, H.; Schleifenbaum, W.

2009-01-01

We study the Hamiltonian approach to 1 + 1 dimensional Yang-Mills theory in Coulomb gauge, considering both the pure Coulomb gauge and the gauge where in addition the remaining constant gauge field is restricted to the Cartan algebra. We evaluate the corresponding Faddeev-Popov determinants, resolve Gauss' law and derive the Hamiltonians, which differ in both gauges due to additional zero modes of the Faddeev-Popov kernel in the pure Coulomb gauge. By Gauss' law the zero modes of the Faddeev-Popov kernel constrain the physical wave functionals to zero colour charge states. We solve the Schroedinger equation in the pure Coulomb gauge and determine the vacuum wave functional. The gluon and ghost propagators and the static colour Coulomb potential are calculated in the first Gribov region as well as in the fundamental modular region, and Gribov copy effects are studied. We explicitly demonstrate that the Dyson-Schwinger equations do not specify the Gribov region while the propagators and vertices do depend on the Gribov region chosen. In this sense, the Dyson-Schwinger equations alone do not provide the full non-abelian quantum gauge theory, but subsidiary conditions must be required. Implications of Gribov copy effects for lattice calculations of the infrared behaviour of gauge-fixed propagators are discussed. We compute the ghost-gluon vertex and provide a sensible truncation of Dyson-Schwinger equations. Approximations of the variational approach to the 3 + 1 dimensional theory are checked by comparison to the 1 + 1 dimensional case

Hamiltonian reduction of Kac-Moody algebras

International Nuclear Information System (INIS)

Kimura, Kazuhiro

1991-01-01

Feigin-Fucks construction provides us methods to treat rational conformal theories in terms of free fields. This formulation enables us to describe partition functions and correlation functions in the Fock space of free fields. There are several attempt extending to supersymmetric theories. In this report authors present an explicit calculation of the Hamiltonian reduction based on the free field realization. In spite of the results being well-known, the relations can be clearly understood in the language of bosons. Authors perform the hamiltonian reduction by imposing a constraint with appropriate gauge transformations which preserve the constraint. This approaches enables us to gives the geometric interpretation of super Virasoro algebras and relations of the super gravity. In addition, author discuss the properties of quantum groups by using the explicit form of the group element. It is also interesting to extend to super Kac-Moody algebras. (M.N.)

Symplectic manifolds, coadjoint orbits, and Mean Field Theory

International Nuclear Information System (INIS)

Rosensteel, G.

1986-01-01

Mean field theory is given a geometrical interpretation as a Hamiltonian dynamical system. The Hartree-Fock phase space is the Grassmann manifold, a symplectic submanifold of the projective space of the full many-fermion Hilbert space. The integral curves of the Hartree-Fock vector field are the time-dependent Hartree-Fock solutions, while the critical points of the energy function are the time-independent states. The mean field theory is generalized beyond determinants to coadjoint orbit spaces of the unitary group; the Grassmann variety is the minimal coadjoint orbit

Hamiltonian term for a uniform dc electric field under the adiabatic approximation

Science.gov (United States)

Siu, Zhuo Bin; Jalil, Mansoor B. A.; Tan, Seng Ghee

2018-02-01

In this work, we show that the disorder-free Kubo formula for the nonequilibrium value of an observable due to a dc electric field, represented by Exx ̂ in the Hamiltonian, can be interpreted as the standard time-independent theory response of the observable due to a time- and position-independent perturbation HMF. We derive the explicit expression for HMF and show that it originates from the adiabatic approximation to Kubo formula and the time-independent perturbation theory, as well as the Sundaram-Niu wave-packet formalism, we show that HMF reproduces the effect of the E field, i.e., Exx ̂ , up to the first order. This replacement suggests the emergence of a spin current term that is not captured by the standard Kubo formula spin current calculation. We illustrate this via the exemplary spin current for the heavy-hole spin-3/2 Luttinger system.

Introduction to thermodynamics of spin models in the Hamiltonian limit

Energy Technology Data Exchange (ETDEWEB)

Berche, Bertrand [Groupe M, Laboratoire de Physique des Materiaux, UMR CNRS No 7556, Universite Henri Poincare, Nancy 1, BP 239, F-54506 Vandoeuvre les Nancy, (France); Lopez, Alexander [Instituto Venezolano de Investigaciones CientIficas, Centro de Fisica, Carr. Panamericana, km 11, Altos de Pipe, Aptdo 21827, 1020-A Caracas, (Venezuela)

2006-01-01

A didactic description of the thermodynamic properties of classical spin systems is given in terms of their quantum counterpart in the Hamiltonian limit. Emphasis is on the construction of the relevant Hamiltonian and the calculation of thermal averages is explicitly done in the case of small systems described, in Hamiltonian field theory, by small matrices. The targeted students are those of a graduate statistical physics course.

Riemannian geometry of Hamiltonian chaos: hints for a general theory.

Science.gov (United States)

Cerruti-Sola, Monica; Ciraolo, Guido; Franzosi, Roberto; Pettini, Marco

2008-10-01

We aim at assessing the validity limits of some simplifying hypotheses that, within a Riemmannian geometric framework, have provided an explanation of the origin of Hamiltonian chaos and have made it possible to develop a method of analytically computing the largest Lyapunov exponent of Hamiltonian systems with many degrees of freedom. Therefore, a numerical hypotheses testing has been performed for the Fermi-Pasta-Ulam beta model and for a chain of coupled rotators. These models, for which analytic computations of the largest Lyapunov exponents have been carried out in the mentioned Riemannian geometric framework, appear as paradigmatic examples to unveil the reason why the main hypothesis of quasi-isotropy of the mechanical manifolds sometimes breaks down. The breakdown is expected whenever the topology of the mechanical manifolds is nontrivial. This is an important step forward in view of developing a geometric theory of Hamiltonian chaos of general validity.

Hamiltonian study of improved U(1) lattice gauge theory in three dimensions

International Nuclear Information System (INIS)

Loan, Mushtaq; Hamer, Chris

2004-01-01

A comprehensive analysis of the Symanzik improved anisotropic three-dimensional U(1) lattice gauge theory in the Hamiltonian limit is made. Monte Carlo techniques are used to obtain numerical results for the static potential, ratio of the renormalized and bare anisotropies, the string tension, lowest glueball masses and the mass ratio. Evidence that rotational symmetry is established more accurately for the Symanzik improved anisotropic action is presented. The discretization errors in the static potential and the renormalization of the bare anisotropy are found to be only a few percent compared to errors of about 20-25 % for the unimproved gauge action. Evidence of scaling in the string tension, antisymmetric mass gap and the mass ratio is observed in the weak coupling region and the behavior is tested against analytic and numerical results obtained in various other Hamiltonian studies of the theory. We find that more accurate determination of the scaling coefficients of the string tension and the antisymmetric mass gap has been achieved, and the agreement with various other Hamiltonian studies of the theory is excellent. The improved action is found to give faster convergence to the continuum limit. Very clear evidence is obtained that in the continuum limit the glueball ratio M S /M A approaches exactly 2, as expected in a theory of free, massive bosons

The general theory of quantized fields in the 1950s

International Nuclear Information System (INIS)

Wightman, A.S.

1989-01-01

This review describes developments in theoretical particle physics in the 1950s which were important in the race to develop a putative general theory of quantized fields, especially ideas that offered a mathematically rigorous theory. Basic theoretical concepts then available included the Hamiltonian formulation of quantum dynamics, canonical quantization, perturbative renormalization theory and the theory of distributions. Following a description of various important theoretical contributions of this era, the review ends with a summary of the most important contributions of axiomatic field theory to concrete physics applications. (UK)

Quantum field theory on higher-genus Riemann surfaces

International Nuclear Information System (INIS)

Kubo, Reijiro; Yoshii, Hisahiro; Ojima, Shuichi; Paul, S.K.

1989-07-01

Quantum field theory for b-c systems is formulated on Riemann surfaces with arbitrary genus. We make use of the formalism recently developed by Krichever and Novikov. Hamiltonian is defined properly, and the Ward-Takahashi identities are derived on higher-genus Riemann surfaces. (author)

Quantum field theory of photon—Dirac fermion interacting system in graphene monolayer

International Nuclear Information System (INIS)

Nguyen, Bich Ha; Nguyen, Van Hieu

2016-01-01

The purpose of the present work is to elaborate quantum field theory of interacting systems comprising Dirac fermion fields in a graphene monolayer and the electromagnetic field. Since the Dirac fermions are confined in a two-dimensional plane, the interaction Hamiltonian of this system contains the projection of the electromagnetic field operator onto the plane of a graphene monolayer. Following the quantization procedure in traditional quantum electrodynamics we chose to work in the gauge determined by the weak Lorentz condition imposed on the state vectors of all physical states of the system. The explicit expression of the two-point Green function of the projection onto a graphene monolayer of a free electromagnetic field is derived. This two-point Green function and the expression of the interaction Hamiltonian together with the two-point Green functions of free Dirac fermion fields established in our previous work form the basics of the perturbation theory of the above-mentioned interacting field system. As an example, the perturbation theory is applied to the study of two-point Green functions of this interacting system of quantum fields. (paper)

Nuclear properties with realistic Hamiltonians through spectral distribution theory

International Nuclear Information System (INIS)

Vary, J.P.; Belehrad, R.; Dalton, B.J.

1979-01-01

Motivated by the need of non-perturbative methods for utilizing realistic nuclear Hamiltonians H, the authors use spectral distribution theory, based on calculated moments of H, to obtain specific bulk and valence properties of finite nuclei. The primary emphasis here is to present results for the binding energies of nuclei obtained with and without an assumed core. (Auth.)

Integrable systems and quantum field theory. Works in progress Nr 75

International Nuclear Information System (INIS)

Baird, Paul; Helein, Frederic; Kouneiher, Joseph; Roubtsov, Volodya; Antunes, Paulo; Banos, Bertrand; Barbachoux, Cecile; Desideri, Laura; Kahouadji, Nabil; Gerding, Aaron; Heller, Sebastian; Schmitt, Nicholas; Harrivel, Dikanaina; Hoevenaars, Luuk K.; Iftime, Mihaela; Levy, Thierry; Lisovyy, Oleg; Masson, Thierry; Skrypnyk, Taras; Pedit, Franz; Egeileh, Michel

2009-01-01

The contributions of this collective book address the quantum field theory (integrable systems and quantum field theory, introduction to supermanifolds and supersymmetry, beyond geometric quantification, Gaussian measurements and Fock spaces), differential geometry and physics (gravitation and geometry, physical events and the superspace about the hole argument, the Cartan-Kaehler theory and applications to local isometric and conformal embedding, calibrations, Cabal-Yau structures and Monge-Ampere structures, Hamiltonian multi-symplectic formalism and Monge-Ampere equations, big bracket, derivations and derivative multi-brackets), integrable system, geometry and physics (finite-volume correlation functions of monodromy fields on the lattice with the Toeplitz representation, Frobenius manifolds and algebraic integrability, an introduction to twistors, Hamiltonian systems on the 'coupled' curves, Nambu-Poisson mechanics and Fairlie-type integrable systems, minimal surfaces with polygonal boundary and Fuchsian equations, global aspects of integrable surface geometry), and non commutative geometry (an informal introduction to the ideas and concepts of non commutative geometry)

A general action for topological quantum field theories

International Nuclear Information System (INIS)

Dayi, O.F.

1989-03-01

Topological field theories can be formulated by beginning from a higher dimensional action. The additional dimension is an unphysical time parameter and the action is the derivative of a functional W with respect to this variable. In the d = 4 case, it produces actions which are shown to give topological quantum field theory after gauge fixing. In d = 3 this action leads to the Hamiltonian, which yields the Floer groups if the additional parameter is treated as physical when W is the pure Chern-Simons action. This W can be used to define a topological quantum field theory in d = 3 by treating the additional parameter as unphysical. The BFV-BRST operator quantization of this theory yields to an enlarged system which has only first class constraints. This is not identical to the previously introduced d = 3 topological quantum field theory, even if it is shown that the latter theory also gives the theory which we began with, after a partial gauge fixing. (author). 18 refs

NLO renormalization in the Hamiltonian truncation

Science.gov (United States)

Elias-Miró, Joan; Rychkov, Slava; Vitale, Lorenzo G.

2017-09-01

Hamiltonian truncation (also known as "truncated spectrum approach") is a numerical technique for solving strongly coupled quantum field theories, in which the full Hilbert space is truncated to a finite-dimensional low-energy subspace. The accuracy of the method is limited only by the available computational resources. The renormalization program improves the accuracy by carefully integrating out the high-energy states, instead of truncating them away. In this paper, we develop the most accurate ever variant of Hamiltonian Truncation, which implements renormalization at the cubic order in the interaction strength. The novel idea is to interpret the renormalization procedure as a result of integrating out exactly a certain class of high-energy "tail states." We demonstrate the power of the method with high-accuracy computations in the strongly coupled two-dimensional quartic scalar theory and benchmark it against other existing approaches. Our work will also be useful for the future goal of extending Hamiltonian truncation to higher spacetime dimensions.

Hamiltonian theory of vacuum helical torus lines of magnetic force

International Nuclear Information System (INIS)

Gnudi, Giovanni; Hatori, Tadatsugu

1994-01-01

For making plasma into equilibrium state, the lines of magnetic force must have magnetic surfaces. However in a helical system, space is divided into the region having magnetic surface structure and the region that does not have it. Accordingly, it is an important basic research for the plasma confinement in a helical system to examine where is the boundary of both regions and how is the large area structure of the lines of magnetic force in the boundary region. The lines of magnetic force can be treated as a Hamilton mechanics system, and it has been proved that the Hamiltonian for the lines of magnetic force can be expressed by a set of canonical variables and the function of time. In this research, the Hamiltonian that describes the lines of magnetic force of helical system torus coordination in vacuum was successfully determined concretely. Next, the development of new linear symplectic integration method was carried out. The important supports for the theory of determining Hamiltonian are Lie transformation and paraxial expansion. The procedure is explained. In Appendix, Lie transformation, Hamiltonian for the lines of magnetic force, magnetic potential, Taylor expansion of the potential, cylindrical limit approximation, helical toroidal potential and integrable model are described. (K.I.)

Light-front quantized field theory (an introduction): spontaneous symmetry breaking. Phase transition in φ4 theory

International Nuclear Information System (INIS)

Srivastava, Prem P.

1994-01-01

The Dirac procedure is used to construct the Hamiltonian formulation of the scalar field theory on the light-front. The theory is quantized and the mechanism of the spontaneous symmetry breaking in the front form and the instant form dynamics are compared. The phase transition in (φ 4 )2 theory is also discussed and found to be of the second order. (author). 36 refs

Symmetry-adaptation and selection rules for effective crystal field Hamiltonians

International Nuclear Information System (INIS)

Tuszynski, J.A.

1986-01-01

The intention of this paper is to systematically derive an effective Hamiltonian in the presence of crystal fields in such a way as to incorporate relativistic effects and higher order perturbation corrections including configuration mixing. This Hamiltonian will then be conveniently represented as a symmetry-adapted series of one- and two-body double tensor operators whose matrix elements will be analyzed for selection rules. 16 references, 4 tables

Transversity results and computations in symplectic field theory

International Nuclear Information System (INIS)

Fabert, Oliver

2008-01-01

Although the definition of symplectic field theory suggests that one has to count holomorphic curves in cylindrical manifolds R x V equipped with a cylindrical almost complex structure J, it is already well-known from Gromov-Witten theory that, due to the presence of multiply-covered curves, we in general cannot achieve transversality for all moduli spaces even for generic choices of J. In this thesis we treat the transversality problem of symplectic field theory in two important cases. In the first part of this thesis we are concerned with the rational symplectic field theory of Hamiltonian mapping tori, which is also called the Floer case. For this observe that in the general geometric setup for symplectic field theory, the contact manifolds can be replaced by mapping tori M φ of symplectic manifolds (M,ω M ) with symplectomorphisms φ. While the cylindrical contact homology of M φ is given by the Floer homologies of powers of φ, the other algebraic invariants of symplectic field theory for M φ provide natural generalizations of symplectic Floer homology. For symplectically aspherical M and Hamiltonian φ we study the moduli spaces of rational curves and prove a transversality result, which does not need the polyfold theory by Hofer, Wysocki and Zehnder and allows us to compute the full contact homology of M φ ≅ S 1 x M. The second part of this thesis is devoted to the branched covers of trivial cylinders over closed Reeb orbits, which are the trivial examples of punctured holomorphic curves studied in rational symplectic field theory. Since all moduli spaces of trivial curves with virtual dimension one cannot be regular, we use obstruction bundles in order to find compact perturbations making the Cauchy-Riemann operator transversal to the zero section and show that the algebraic count of elements in the resulting regular moduli spaces is zero. Once the analytical foundations of symplectic field theory are established, our result implies that the

Quantum Monte Carlo studies in Hamiltonian lattice gauge theory

International Nuclear Information System (INIS)

Hamer, C.J.; Samaras, M.; Bursill, R.J.

2000-01-01

Full text: The application of Monte Carlo methods to the 'Hamiltonian' formulation of lattice gauge theory has been somewhat neglected, and lags at least ten years behind the classical Monte Carlo simulations of Euclidean lattice gauge theory. We have applied a Green's Function Monte Carlo algorithm to lattice Yang-Mills theories in the Hamiltonian formulation, combined with a 'forward-walking' technique to estimate expectation values and correlation functions. In this approach, one represents the wave function in configuration space by a discrete ensemble of random walkers, and application of the time development operator is simulated by a diffusion and branching process. The approach has been used to estimate the ground-state energy and Wilson loop values in the U(1) theory in (2+1)D, and the SU(3) Yang-Mills theory in (3+1)D. The finite-size scaling behaviour has been explored, and agrees with the predictions of effective Lagrangian theory, and weak-coupling expansions. Crude estimates of the string tension are derived, which agree with previous results at intermediate couplings; but more accurate results for larger loops will be required to establish scaling behaviour at weak couplings. A drawback to this method is that it is necessary to introduce a 'trial' or 'guiding wave function' to guide the walkers towards the most probable regions of configuration space, in order to achieve convergence and accuracy. The 'forward-walking' estimates should be independent of this guidance, but in fact for the SU(3) case they turn out to be sensitive to the choice of trial wave function. It would be preferable to use some sort of Metropolis algorithm instead to produce a correct distribution of walkers: this may point in the direction of a Path Integral Monte Carlo approach

Gauge-invariant variational methods for Hamiltonian lattice gauge theories

International Nuclear Information System (INIS)

Horn, D.; Weinstein, M.

1982-01-01

This paper develops variational methods for calculating the ground-state and excited-state spectrum of Hamiltonian lattice gauge theories defined in the A 0 = 0 gauge. The scheme introduced in this paper has the advantage of allowing one to convert more familiar tools such as mean-field, Hartree-Fock, and real-space renormalization-group approximation, which are by their very nature gauge-noninvariant methods, into fully gauge-invariant techniques. We show that these methods apply in the same way to both Abelian and non-Abelian theories, and that they are at least powerful enough to describe correctly the physics of periodic quantum electrodynamics (PQED) in (2+1) and (3+1) space-time dimensions. This paper formulates the problem for both Abelian and non-Abelian theories and shows how to reduce the Rayleigh-Ritz problem to that of computing the partition function of a classical spin system. We discuss the evaluation of the effective spin problem which one derives the PQED and then discuss ways of carrying out the evaluation of the partition function for the system equivalent to a non-Abelian theory. The explicit form of the effective partition function for the non-Abelian theory is derived, but because the evaluation of this function is considerably more complicated than the one derived in the Abelian theory no explicit evaluation of this function is presented. However, by comparing the gauge-projected Hartree-Fock wave function for PQED with that of the pure SU(2) gauge theory, we are able to show that extremely interesting differences emerge between these theories even at this simple level. We close with a discussion of fermions and a discussion of how one can extend these ideas to allow the computation of the glueball and hadron spectrum

A new look at the free electromagnetic field. The Gauss law as a hamiltonian equation of motion

International Nuclear Information System (INIS)

Aldaya, V.; Navarro-Salas, J.

1992-01-01

A new canonical formalism for the free electromagnetic field is proposed in terms of an infinite-dimensional Lie group. The Gauss law is derived as a hamiltonian equation of motion and the quantum theory is obtained by constructing the irreducible representation of the group. The quantum Gauss law thus appears as an additional polarization equation and not as a constraint equation. (orig.)

A Hamiltonian structure for the linearized Einstein vacuum field equations

International Nuclear Information System (INIS)

Torres del Castillo, G.F.

1991-01-01

By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained (Author)

Hamiltonian formulation of QCD in the Schwinger gauge

International Nuclear Information System (INIS)

Schutte, D.

1989-01-01

The structure of the Hamiltonian related to a regularized non-Abelian gauge field theory is discussed in the light of different choices for gauge-invariant wave functionals (loop space, Coulomb, axial, Schwinger gauge). Arguments are given for the suggestion that the Schwinger gauge offers a specially suited framework for the computation of bound-state (hadron) properties. The most important reasons are the manifest rotation invariance, the lack of a Gribov horizon (giving standard many-body techniques a better chance), and the fact that a regularization analogous to the lattice regularization is easily implementable. Some details of the Schwinger-gauge Hamiltonian theory are discussed

Small traveling clusters in attractive and repulsive Hamiltonian mean-field models.

Science.gov (United States)

Barré, Julien; Yamaguchi, Yoshiyuki Y

2009-03-01

Long-lasting small traveling clusters are studied in the Hamiltonian mean-field model by comparing between attractive and repulsive interactions. Nonlinear Landau damping theory predicts that a Gaussian momentum distribution on a spatially homogeneous background permits the existence of traveling clusters in the repulsive case, as in plasma systems, but not in the attractive case. Nevertheless, extending the analysis to a two-parameter family of momentum distributions of Fermi-Dirac type, we theoretically predict the existence of traveling clusters in the attractive case; these findings are confirmed by direct N -body numerical simulations. The parameter region with the traveling clusters is much reduced in the attractive case with respect to the repulsive case.

A Hamiltonian approach to model and analyse networks of ...

Indian Academy of Sciences (India)

2015-09-24

Sep 24, 2015 ... Gyroscopes; energy harvesters; synchronization; Hamiltonian mechanics. ... ideas and methods from nonlinear dynamics system theory, in particular, ... deploy highly sensitive, lowpower, magnetic and electric field sensors.

Hamiltonian description of the parametrized scalar field in bounded spatial regions

International Nuclear Information System (INIS)

Barbero G, J Fernando; Margalef-Bentabol, Juan; Villaseñor, Eduardo J S

2016-01-01

We study the Hamiltonian formulation for a parametrized scalar field in a regular bounded spatial region subject to Dirichlet, Neumann and Robin boundary conditions. We generalize the work carried out by a number of authors on parametrized field systems to the interesting case where spatial boundaries are present. The configuration space of our models contains both smooth scalar fields defined on the spatial manifold and spacelike embeddings from the spatial manifold to a target spacetime endowed with a fixed Lorentzian background metric. We pay particular attention to the geometry of the infinite dimensional manifold of embeddings and the description of the relevant geometric objects: the symplectic form on the primary constraint submanifold and the Hamiltonian vector fields defined on it. (paper)

Theory of superconducting tunneling without the tunneling Hamiltonian

International Nuclear Information System (INIS)

Arnold, G.B.

1987-01-01

When a tunneling barrier is nearly transparent, the standard tunneling (or transfer) Hamiltonian approximation fails. The author describes the theory which is necessary for calculating the tunneling current in these cases, and illustrate it by comparing theory and experiment on superconductor/insulator/superconductor (SIS) junctions have ultra-thin tunnel barriers. This theory accurately explains the subgap structure which appears in the dynamical resistance of such SIS junctions, including many observed details which no previous theory has reproduced. The expression for the current through an SIS junction with an ultrathin barrier is given by I(t) = Re{Sigma/sub n/ J/sub n/ (omega/sub o/)e/sup in omega/o/sup t/} where omega/sub o/ = 2eV/h is the Josephson frequency, V is the bias voltage, and the J/sub n/ are voltage dependent coefficients, one for each positive or negative integer, n, and n=0. The relative sign of the terms involving cos(n omega/sub o/t) and sin(n omega/sub o/t) agrees with experiment, in contrast to previous theories of Josephson tunneling

Hamiltonian closures in fluid models for plasmas

Science.gov (United States)

Tassi, Emanuele

2017-11-01

This article reviews recent activity on the Hamiltonian formulation of fluid models for plasmas in the non-dissipative limit, with emphasis on the relations between the fluid closures adopted for the different models and the Hamiltonian structures. The review focuses on results obtained during the last decade, but a few classical results are also described, in order to illustrate connections with the most recent developments. With the hope of making the review accessible not only to specialists in the field, an introduction to the mathematical tools applied in the Hamiltonian formalism for continuum models is provided. Subsequently, we review the Hamiltonian formulation of models based on the magnetohydrodynamics description, including those based on the adiabatic and double adiabatic closure. It is shown how Dirac's theory of constrained Hamiltonian systems can be applied to impose the incompressibility closure on a magnetohydrodynamic model and how an extended version of barotropic magnetohydrodynamics, accounting for two-fluid effects, is amenable to a Hamiltonian formulation. Hamiltonian reduced fluid models, valid in the presence of a strong magnetic field, are also reviewed. In particular, reduced magnetohydrodynamics and models assuming cold ions and different closures for the electron fluid are discussed. Hamiltonian models relaxing the cold-ion assumption are then introduced. These include models where finite Larmor radius effects are added by means of the gyromap technique, and gyrofluid models. Numerical simulations of Hamiltonian reduced fluid models investigating the phenomenon of magnetic reconnection are illustrated. The last part of the review concerns recent results based on the derivation of closures preserving a Hamiltonian structure, based on the Hamiltonian structure of parent kinetic models. Identification of such closures for fluid models derived from kinetic systems based on the Vlasov and drift-kinetic equations are presented, and

Lagrangian and Hamiltonian dynamics

CERN Document Server

Mann, Peter

2018-01-01

An introductory textbook exploring the subject of Lagrangian and Hamiltonian dynamics, with a relaxed and self-contained setting. Lagrangian and Hamiltonian dynamics is the continuation of Newton's classical physics into new formalisms, each highlighting novel aspects of mechanics that gradually build in complexity to form the basis for almost all of theoretical physics. Lagrangian and Hamiltonian dynamics also acts as a gateway to more abstract concepts routed in differential geometry and field theories and can be used to introduce these subject areas to newcomers. Journeying in a self-contained manner from the very basics, through the fundamentals and onwards to the cutting edge of the subject, along the way the reader is supported by all the necessary background mathematics, fully worked examples, thoughtful and vibrant illustrations as well as an informal narrative and numerous fresh, modern and inter-disciplinary applications. The book contains some unusual topics for a classical mechanics textbook. Mo...

On the consistency of quantum geometrodynamics and quantum field theories in the Bohm-de Broglie Interpretation

Energy Technology Data Exchange (ETDEWEB)

Pinto-Neto, N.; Santini, E. Sergio. E-mail: nelsonpn@lafex.cbpf.br; santini@lafex.cbpf.br

2000-12-01

We consider quantum geometrodynamics and parametrized quantum field theories in the frame-work of the Bohm-de Broglie interpretation. In the first case, and following the lines of our previous work, where a Hamiltonian formalism for the bohmian trajectories was constructed, we show the consistency of the theory for any quantum potential, completing the scenarios for canonical quantum cosmology presented there. In the latter case, we prove the consistency of scalar field theory in Minkowski spacetime for any quantum potential, and we show, using this alternative Hamiltonian method, a concrete example already known in the literature where Lorentz invariance of individual events is broken. (author)

Unambiguous formalism for higher order Lagrangian field theories

International Nuclear Information System (INIS)

Campos, Cedric M; De Leon, Manuel; De Diego, David MartIn; Vankerschaver, Joris

2009-01-01

The aim of this paper is to propose an unambiguous intrinsic formalism for higher order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, and implies the existence of different Cartan forms and Legendre transformations. We propose a differential-geometric setting for the dynamics of a higher order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher order jet bundle and the canonical multisymplectic form on its affine dual. As both of these objects are uniquely defined, the Skinner-Rusk approach has the advantage that it does not suffer from the arbitrariness in conventional descriptions. The result is that we obtain a unique and global intrinsic version of the Euler-Lagrange equations for higher order field theories. Several examples illustrate our construction.

Integrable Hamiltonian systems and interactions through quadratic constraints

International Nuclear Information System (INIS)

Pohlmeyer, K.

1975-08-01

Osub(n)-invariant classical relativistic field theories in one time and one space dimension with interactions that are entirely due to quadratic constraints are shown to be closely related to integrable Hamiltonian systems. (orig.) [de

Analytic operator approach to fermionic lattice field theories

International Nuclear Information System (INIS)

Duncan, A.

1985-01-01

An analytic Lanczos algorithm previously used to extract the spectrum of bosonic lattice field theories in the continuum region is extended to theories with fermions. The method is illustrated in detail for the (1+1)-dimensional Gross-Neveu model. All parameters in the model (coupling, lattice size N, number of fermion flavors Nsub(F), etc.) appear explicitly in analytic formulas for matrix elements of the hamiltonian. The method is applied to the calculation of the collective field vacuum expectation value and the mass gap, and excellent agreement obtained with explicit results available from the large Nsub(F) solution of the model. (orig.)

A Hamiltonian five-field gyrofluid model

Energy Technology Data Exchange (ETDEWEB)

Keramidas Charidakos, I.; Waelbroeck, F. L.; Morrison, P. J. [Institute for Fusion Studies and Department of Physics, The University of Texas at Austin, Austin, TX 78712 (United States)

2015-11-15

A Lie-Poisson bracket is presented for a five-field gyrofluid model, thereby showing the model to be Hamiltonian. The model includes the effects of magnetic field curvature and describes the evolution of the electron and ion gyro-center densities, the parallel component of the ion and electron velocities, and the ion temperature. The quasineutrality property and Ampère's law determine, respectively, the electrostatic potential and magnetic flux. The Casimir invariants are presented, and shown to be associated with five Lagrangian invariants advected by distinct velocity fields. A linear, local study of the model is conducted both with and without Landau and diamagnetic resonant damping terms. Stability criteria and dispersion relations for the electrostatic and the electromagnetic cases are derived and compared with their analogs for fluid and kinetic models.

Nonconformal scalar field in uniform isotropic space and the method of Hamiltonian diagonalization

International Nuclear Information System (INIS)

Pavlov, Yu.V.

2001-01-01

One diagonalized metric Hamiltonian of scalar field with arbitrary relation with curvature in N-dimensional uniform isotropic space. One derived spectrum of energies of the appropriate quasi-particles. One calculated energy of quasi-particle appropriate to the canonical Hamiltonian diagonal shape. One structured a modified tensor of energy-pulse with the following features. In case of conformal scalar field it coincides with the metric tensor of energy-pulse. When it is diagonalized the energies of the appropriate particles of nonconformal field are equal to oscillation frequency and the number of such particles produced in non-stationary metric is the finite one. It is shown that Hamiltonian calculated on the basis of the modified tensor of energy-pulse may be derived as a canonical one at certain selection of variables [ru

Hamiltonian description of the ideal fluid

International Nuclear Information System (INIS)

Morrison, P.J.

1998-01-01

The Hamiltonian viewpoint of fluid mechanical systems with few and infinite number of degrees of freedom is described. Rudimentary concepts of finite-degree-of-freedom Hamiltonian dynamics are reviewed, in the context of the passive advection of a scalar or tracer field by a fluid. The notions of integrability, invariant-tori, chaos, overlap criteria, and invariant-tori breakup are described in this context. Preparatory to the introduction of field theories, systems with an infinite number of degrees of freedom, elements of functional calculus and action principles of mechanics are reviewed. The action principle for the ideal compressible fluid is described in terms of Lagrangian or material variables. Hamiltonian systems in terms of noncanonical variables are presented, including several examples of Eulerian or inviscid fluid dynamics. Lie group theory sufficient for the treatment of reduction is reviewed. The reduction from Lagrangian to Eulerian variables is treated along with Clebsch variable decompositions. Stability in the canonical and noncanonical Hamiltonian contexts is described. Sufficient conditions for stability, such as Rayleigh-like criteria, are seen to be only sufficient in the general case because of the existence of negative-energy modes, which are possessed by interesting fluid equilibria. Linearly stable equilibria with negative energy modes are argued to be unstable when nonlinearity or dissipation is added. The energy-Casimir method is discussed and a variant of it that depends upon the notion of dynamical accessibility is described. The energy content of a perturbation about a general fluid equilibrium is calculated using three methods. copyright 1998 The American Physical Society

Transversity results and computations in symplectic field theory

Energy Technology Data Exchange (ETDEWEB)

Fabert, Oliver

2008-02-21

Although the definition of symplectic field theory suggests that one has to count holomorphic curves in cylindrical manifolds R x V equipped with a cylindrical almost complex structure J, it is already well-known from Gromov-Witten theory that, due to the presence of multiply-covered curves, we in general cannot achieve transversality for all moduli spaces even for generic choices of J. In this thesis we treat the transversality problem of symplectic field theory in two important cases. In the first part of this thesis we are concerned with the rational symplectic field theory of Hamiltonian mapping tori, which is also called the Floer case. For this observe that in the general geometric setup for symplectic field theory, the contact manifolds can be replaced by mapping tori M{sub {phi}} of symplectic manifolds (M,{omega}{sub M}) with symplectomorphisms {phi}. While the cylindrical contact homology of M{sub {phi}} is given by the Floer homologies of powers of {phi}, the other algebraic invariants of symplectic field theory for M{sub {phi}} provide natural generalizations of symplectic Floer homology. For symplectically aspherical M and Hamiltonian {phi} we study the moduli spaces of rational curves and prove a transversality result, which does not need the polyfold theory by Hofer, Wysocki and Zehnder and allows us to compute the full contact homology of M{sub {phi}} {approx_equal} S{sup 1} x M. The second part of this thesis is devoted to the branched covers of trivial cylinders over closed Reeb orbits, which are the trivial examples of punctured holomorphic curves studied in rational symplectic field theory. Since all moduli spaces of trivial curves with virtual dimension one cannot be regular, we use obstruction bundles in order to find compact perturbations making the Cauchy-Riemann operator transversal to the zero section and show that the algebraic count of elements in the resulting regular moduli spaces is zero. Once the analytical foundations of symplectic

Long-range interactions in lattice field theory

International Nuclear Information System (INIS)

Rabin, J.M.

1981-06-01

Lattice quantum field theories containing fermions can be formulated in a chirally invariant way provided long-range interactions are introduced. It is established that in weak-coupling perturbation theory such a lattice theory is renormalizable when the corresponding continuum theory is, and that the continuum theory is indeed recovered in the perturbative continuum limit. In the strong-coupling limit of these theories one is led to study an effective Hamiltonian describing a Heisenberg antiferromagnet with long-range interactions. Block-spin renormalization group methods are used to find a critical rate of falloff of the interactions, approximately as inverse distance squared, which separates a nearest-neighbor-antiferromagnetic phase from a phase displaying identifiable long-range effects. A duality-type symmetry is present in some block-spin calculations

Long-range interactions in lattice field theory

Energy Technology Data Exchange (ETDEWEB)

Rabin, J.M.

1981-06-01

Lattice quantum field theories containing fermions can be formulated in a chirally invariant way provided long-range interactions are introduced. It is established that in weak-coupling perturbation theory such a lattice theory is renormalizable when the corresponding continuum theory is, and that the continuum theory is indeed recovered in the perturbative continuum limit. In the strong-coupling limit of these theories one is led to study an effective Hamiltonian describing a Heisenberg antiferromagnet with long-range interactions. Block-spin renormalization group methods are used to find a critical rate of falloff of the interactions, approximately as inverse distance squared, which separates a nearest-neighbor-antiferromagnetic phase from a phase displaying identifiable long-range effects. A duality-type symmetry is present in some block-spin calculations.

Existence of 121 limit cycles in a perturbed planar polynomial Hamiltonian vector field of degree 11

International Nuclear Information System (INIS)

Wang, S.; Yu, P.

2006-01-01

In this article, a systematic procedure has been explored to studying general Z q -equivariant planar polynomial Hamiltonian vector fields for the maximal number of closed orbits and the maximal number of limit cycles after perturbation. Following the procedure by taking special consideration of Z 12 -equivariant vector fields of degree 11, the maximal of 99 closed orbits are obtained under a well-defined coefficient group. Consequently, perturbation parameter control in limit cycle computation leads to the existence of 121 limit cycles in the perturbed Hamiltonian vector field, which gives rise to the lower bound of Hilbert number of 11th-order systems as H(11) ≥ 11 2 . Two conjectures are proposed regarding the maximal number of closed orbits for equivariant polynomial Hamiltonian vector fields and the maximal number of limit cycles bifurcated from the well defined Hamiltonian vector fields after perturbation

Exact spinor-scalar bound states in a quantum field theory with scalar interactions

International Nuclear Information System (INIS)

Shpytko, Volodymyr; Darewych, Jurij

2001-01-01

We study two-particle systems in a model quantum field theory in which scalar particles and spinor particles interact via a mediating scalar field. The Lagrangian of the model is reformulated by using covariant Green's functions to solve for the mediating field in terms of the particle fields. This results in a Hamiltonian in which the mediating-field propagator appears directly in the interaction term. It is shown that exact two-particle eigenstates of the Hamiltonian can be determined. The resulting relativistic fermion-boson equation is shown to have Dirac and Klein-Gordon one-particle limits. Analytical solutions for the bound state energy spectrum are obtained for the case of massless mediating fields

Combinatorial quantization of the Hamiltonian Chern-Simons theory

International Nuclear Information System (INIS)

Alekseev, A.Yu.; Grosse, H.; Schomerus, V.

1996-01-01

This paper further develops the combinatorial approach to quantization of the Hamiltonian Chern Simons theory. Using the theory of quantum Wilson lines, we show how the Verlinde algebra appears within the context of quantum group gauge theory. This allows to discuss flatness of quantum connections so that we can give a mathematically rigorous definition of the algebra of observables A CS of the Chern Simons model. It is a *-algebra of ''functions on the quantum moduli space of flat connections'' and comes equipped with a positive functional ω (''integration''). We prove that this data does not depend on the particular choices which have been made in the construction. The algebra A CS provides a deformation quantization of the algebra of functions on the moduli space along the natural Poisson bracket induced by the Chern Simons action. We evaluate a volume of the quantized moduli space and prove that it coincides with the Verlinde number. This answer is also interpreted as a partition partition function of the lattice Yang-Mills theory corresponding to a quantum gauge group. (orig.). With 1 fig

On the physical applications of hyper-Hamiltonian dynamics

International Nuclear Information System (INIS)

Gaeta, Giuseppe; Rodriguez, Miguel A

2008-01-01

An extension of Hamiltonian dynamics, defined on hyper-Kahler manifolds ('hyper-Hamiltonian dynamics') and sharing many of the attractive features of standard Hamiltonian dynamics, was introduced in previous work. In this paper, we discuss applications of the theory to physically interesting cases, dealing with the dynamics of particles with spin 1/2 in a magnetic field, i.e. the Pauli and the Dirac equations. While the free Pauli equation corresponds to a hyper-Hamiltonian flow, it turns out that the hyper-Hamiltonian description of the Dirac equation, and of the full Pauli one, is in terms of two commuting hyper-Hamiltonian flows. In this framework one can use a factorization principle discussed here (which is a special case of a general phenomenon studied by Walcher) and provide an explicit description of the resulting flow. On the other hand, by applying the familiar Foldy-Wouthuysen and Cini-Tousheck transformations (and the one recently introduced by Mulligan) which separate-in suitable limits-the Dirac equation into two equations, each of these turn out to be described by a single hyper-Hamiltonian flow. Thus the hyper-Hamiltonian construction is able to describe the fundamental dynamics for particles with spin

Time and a physical Hamiltonian for quantum gravity.

Science.gov (United States)

Husain, Viqar; Pawłowski, Tomasz

2012-04-06

We present a nonperturbative quantization of general relativity coupled to dust and other matter fields. The dust provides a natural time variable, leading to a physical Hamiltonian with spatial diffeomorphism symmetry. The surprising feature is that the Hamiltonian is not a square root. This property, together with the kinematical structure of loop quantum gravity, provides a complete theory of quantum gravity, and puts applications to cosmology, quantum gravitational collapse, and Hawking radiation within technical reach. © 2012 American Physical Society

Unitarity condition in covariant quantum field theory with indefinite metric

International Nuclear Information System (INIS)

Slavnov, A.A.

1989-01-01

Conditions that ensure the existence of a unitarity S matrix acting on the subspace of states with positive norm are formulated. A study is made of BRST quantization. The only restriction on the class of theories is that the author assumes asymptotic linearization of the theory, namely, that the asymptotic dynamics is determined by a quadratic Hamiltonian. In field theory this is always the case in the framework of standard perturbation theory. However, in some models, for example, string models, and also outside the framework of perturbation theory, this condition need not be satisfied

Relationship between Feshbach's and Green's function theories of the nucleon-nucleus mean field

International Nuclear Information System (INIS)

Capuzzi, F.; Mahaux, C.

1995-01-01

We clarify the relationship and difference between theories of the optical-model potential which had previously been developed in the framework of Feshbach's projection operator approach to nuclear reactions and of Green's function theory, respectively. For definiteness, we consider the nucleon-nucleus system but all results can readily be adapted to the atomic case. The effects of antisymmetrization are properly taken into account. It is shown that one can develop along closely parallel lines the theories of open-quotes holeclose quotes and open-quotes particleclose quotes mean fields. The open-quotes holeclose quotes one-body Hamiltonians describe the single-particle properties of the system formed when one nucleon is taken away from the target ground state, for instance in knockout of pickup processes. The particle one-body Hamiltonians are associated with the system formed when one nucleon is elastically scattered from the ground state, or is added to it by means of stripping reactions. An infinite number of particle, as well as of hole, Hamiltonians are constructed which all yield exactly the same single-particle wave functions. Many open-quotes equivalentclose quotes one-body Hamiltonians can coexist because these operators have a complicated structure: they are nonlocal, complex, and energy-dependent. They do not have the same analytic properties in the complex energy plane. Their real and imaginary parts fulfill dispersion relations which may be different. It is shown that hole and particle Hamiltonians can also be constructed by decomposing any vector of the Hilbert space into two parts which are not orthogonal to one another, in contrast to Feshbach's original theory; one interest of this procedure is that the construction and properties of the corresponding hole Hamiltonian can be justified in a mathematically rigorous way. We exhibit the relationship between the hole and particle Hamiltonians and the open-quotes mass operator.close quotes

arXiv Lightcone Effective Hamiltonians and RG Flows

CERN Document Server

Fitzpatrick, A. Liam; Katz, Emanuel; Vitale, Lorenzo G.; Walters, Matthew T.

We present a prescription for an effective lightcone (LC) Hamiltonian that includes the effects of zero modes, focusing on the case of Conformal Field Theories (CFTs) deformed by relevant operators. We show how the prescription resolves a number of issues with LC quantization, including i) the apparent non-renormalization of the vacuum, ii) discrepancies in critical values of bare parameters in equal-time vs LC quantization, and iii) an inconsistency at large N in CFTs with simple AdS duals. We describe how LC quantization can drastically simplify Hamiltonian truncation methods applied to some large N CFTs, and discuss how the prescription identifies theories where these simplifications occur. We demonstrate and check our prescription in a number of examples.

Hamiltonian formulation of reduced magnetohydrodynamics

International Nuclear Information System (INIS)

Morrison, P.J.; Hazeltine, R.D.

1983-07-01

Reduced magnetohydrodynamics (RMHD) has become a principal tool for understanding nonlinear processes, including disruptions, in tokamak plasmas. Although analytical studies of RMHD turbulence have been useful, the model's impressive ability to simulate tokamak fluid behavior has been revealed primarily by numerical solution. The present work describes a new analytical approach, not restricted to turbulent regimes, based on Hamiltonian field theory. It is shown that the nonlinear (ideal) RMHD system, in both its high-beta and low-beta versions, can be expressed in Hanmiltonian form. Thus a Poisson bracket, [ , ], is constructed such that each RMHD field quantitity, xi/sub i/, evolves according to xi/sub i/ = [xi/sub i/,H], where H is the total field energy. The new formulation makes RMHD accessible to the methodology of Hamiltonian mechanics; it has lead, in particular, to the recognition of new RMHD invariants and even exact, nonlinear RMHD solutions. A canonical version of the Poisson bracket, which requires the introduction of additional fields, leads to a nonlinear variational principle for time-dependent RMHD

Existence of solutions for Hamiltonian field theories by the Hamilton-Jacobi technique

International Nuclear Information System (INIS)

Bruno, Danilo

2011-01-01

The paper is devoted to prove the existence of a local solution of the Hamilton-Jacobi equation in field theory, whence the general solution of the field equations can be obtained. The solution is adapted to the choice of the submanifold where the initial data of the field equations are assigned. Finally, a technique to obtain the general solution of the field equations, starting from the given initial manifold, is deduced.

Single-particle dynamics - Hamiltonian formulation

International Nuclear Information System (INIS)

Montague, B.W.

1977-01-01

In this paper the Hamiltonian formalism is applied to the linear theory of accelerator dynamics. The reasons for the introduction of this method rather than the more straightforward use of second order differential equations of motion are briefly discussed. An outline of Lagrangian and Hamiltonian formalism is given, some properties of the Hamiltonian are discussed and canonical transformations are illustrated. The methods are demonstrated using elementary examples such as the simple pendulum and the procedures adopted to handle specific problems in accelerator theory are indicated. (B.D.)

Hamiltonian field description of two-dimensional vortex fluids and guiding center plasmas

International Nuclear Information System (INIS)

Morrison, P.J.

1981-03-01

The equations that describe the motion of two-dimensional vortex fluids and guiding center plasmas are shown to possess underlying field Hamiltonian structure. A Poisson bracket which is given in terms of the vorticity, the physical although noncanonical dynamical variable, casts these equations into Heisenberg form. The Hamiltonian density is the kinetic energy density of the fluid. The well-known conserved quantities are seen to be in involution with respect to this Poisson bracket. Expanding the vorticity in terms of a Fourier-Dirac series transforms the field description given here into the usual canonical equations for discrete vortex motion. A Clebsch potential representation of the vorticity transforms the noncanonical field description into a canonical description

Axiomatics of Galileo-invariant quantum field theory

International Nuclear Information System (INIS)

Dadashev, L.A.

1986-01-01

The aim of this paper is to construct the axiomatics of Galileo-invariant quantum field theory. The importance of this problem is demonstrated from various points of view: general properties that the fields and observables must satisfy are considered; S-matrix nontriviality of one such model is proved; and the differences from the relativistic case are discussed. The proposed system of axioms is in many respects analogous to Wightman axiomatics, but is less general. The main result is contained in theorems which describe the admissible set of initial fields and total Hamiltonians, i.e., precisely the two entities that completely determine interacting fields. The author considers fields that prove the independence of some axioms

Hamiltonian and Algebraic Theories of Gapped Boundaries in Topological Phases of Matter

Science.gov (United States)

Cong, Iris; Cheng, Meng; Wang, Zhenghan

2017-10-01

We present an exactly solvable lattice Hamiltonian to realize gapped boundaries of Kitaev's quantum double models for Dijkgraaf-Witten theories. We classify the elementary excitations on the boundary, and systematically describe the bulk-to-boundary condensation procedure. We also present the parallel algebraic/categorical structure of gapped boundaries.

Symplectic Geometric Algorithms for Hamiltonian Systems

CERN Document Server

Feng, Kang

2010-01-01

"Symplectic Geometry Algorithms for Hamiltonian Systems" will be useful not only for numerical analysts, but also for those in theoretical physics, computational chemistry, celestial mechanics, etc. The book generalizes and develops the generating function and Hamilton-Jacobi equation theory from the perspective of the symplectic geometry and symplectic algebra. It will be a useful resource for engineers and scientists in the fields of quantum theory, astrophysics, atomic and molecular dynamics, climate prediction, oil exploration, etc. Therefore a systematic research and development

The solutions of affine and conformal affine Toda field theory

International Nuclear Information System (INIS)

Papadopoulos, G.; Spence, B.

1994-02-01

We give new formulations of the solutions of the field equations of the affine Toda and conformal affine Toda theories on a cylinder and two-dimensional Minkowski space-time. These solutions are parameterised in terms of initial data and the resulting covariant phase spaces are diffeomorphic to the Hamiltonian ones. We derive the fundamental Poisson brackets of the parameters of the solutions and give the general static solutions for the affine theory. (authors). 10 refs

Model Hamiltonian Calculations of the Nonlinear Polarizabilities of Conjugated Molecules.

Science.gov (United States)

Risser, Steven Michael

This dissertation advances the theoretical knowledge of the nonlinear polarizabilities of conjugated molecules. The unifying feature of these molecules is an extended delocalized pi electron structure. The pi electrons dominate the electronic properties of the molecules, allowing prediction of molecular properties based on the treatment of just the pi electrons. Two separate pi electron Hamiltonians are used in the research. The principal Hamiltonian used is the non-interacting single-particle Huckel Hamiltonian, which replaces the Coulomb interaction among the pi electrons with a mean field interaction. The simplification allows for exact solution of the Hamiltonian for large molecules. The second Hamiltonian used for this research is the interacting multi-particle Pariser-Parr-Pople (PPP) Hamiltonian, which retains explicit Coulomb interactions. This limits exact solutions to molecules containing at most eight electrons. The molecular properties being investigated are the linear polarizability, and the second and third order hyperpolarizabilities. The hyperpolarizabilities determine the nonlinear optical response of materials. These molecular parameters are determined by two independent approaches. The results from the Huckel Hamiltonian are obtained through first, second and third order perturbation theory. The results from the PPP Hamiltonian are obtained by including the applied field directly in the Hamiltonian and determining the ground state energy at a series of field strengths. By fitting the energy to a polynomial in field strength, the polarizability and hyperpolarizabilities are determined. The Huckel Hamiltonian is used to calculate the third order hyperpolarizability of polyenes. These calculations were the first to show the average hyperpolarizability of the polyenes to be positive, and also to show the saturation of the hyperpolarizability. Comparison of these Huckel results to those from the PPP Hamiltonian shows the lack of explicit Coulomb

The iteration formula of the Maslov-type index theory with applications to nonlinear Hamiltonian systems

International Nuclear Information System (INIS)

Di Dong; Yiming Long.

1994-10-01

In this paper, the iteration formula of the Maslov-type index theory for linear Hamiltonian systems with continuous periodic and symmetric coefficients is established. This formula yields a new method to determine the minimality of the period for solutions of nonlinear autonomous Hamiltonian systems via their Maslov-type indices. Applications of this formula give new results on the existence of periodic solutions with prescribed minimal period for such systems. (author). 40 refs

Metric quantum field theory: A preliminary look

International Nuclear Information System (INIS)

Watson, W.N.

1988-01-01

Spacetime coordinates are involved in uncertainty relations; spacetime itself appears to exhibit curvature. Could the continua associated with field variables exhibit curvature? This question, as well as the ideas that (a) difficulties with quantum theories of gravitation may be due to their formulation in an incorrect analogy with other quantum field theories, (b) spacetime variables should not be any more basic than others for describing physical phenomena, and (c) if field continua do not exhibit curvature, the reasons would be of interest, motivated the formulation of a theory of variable curvature and torsion in the electromagnetic four-potential's reciprocal space. Curvature and torsion equation completely analogous to those for a gauge theory of gravitation (the Einstein-Cartan-Sciama-Kibble theory) are assumed for this continuum. The interaction-Hamiltonian density of this theory, to a first approximation, implies that in addition to the Maxwell-Dirac field interaction of ordinary quantum electrodynamics, there should also be an interaction between Dirac-field vector and pseudovector currents unmediated by photons, as well as other interactions involving two or three Dirac-field currents interacting with the Maxwell field at single spacetime events. Calculations expressing Bhabha-scattering cross sections for incident beams with parallel spins differ from those of unmodified quantum electrodynamics by terms of first order in the gravitational constant of the theory, but the corresponding cross section for unpolarized incident beams differs from that of the unmodified theory only by terms of higher order in that constant. Undesirable features of the present theory include its nonrenormalizability, the obscurity of the meaning of its inverse field operator, and its being based on electrodynamics rather than electroweak dynamics

Momentum and hamiltonian in complex action theory

DEFF Research Database (Denmark)

Nagao, Keiichi; Nielsen, Holger Frits Bech

2012-01-01

$-parametrized wave function, which is a solution to an eigenvalue problem of a momentum operator $\\hat{p}$, in FPI with a starting Lagrangian. Solving the eigenvalue problem, we derive the momentum and Hamiltonian. Oppositely, starting from the Hamiltonian we derive the Lagrangian in FPI, and we are led...

On Distributed Port-Hamiltonian Process Systems

NARCIS (Netherlands)

Lopezlena, Ricardo; Scherpen, Jacquelien M.A.

2004-01-01

In this paper we use the term distributed port-Hamiltonian Process Systems (DPHPS) to refer to the result of merging the theory of distributed Port-Hamiltonian systems (DPHS) with the theory of process systems (PS). Such concept is useful for combining the systematic interconnection of PHS with the

Particle versus field structure in conformal quantum field theories

International Nuclear Information System (INIS)

Schroer, Bert

2000-06-01

I show that a particle structure in conformal field theory is incompatible with interactions. As a substitute one has particle-like excitations whose interpolating fields have in addition to their canonical dimension an anomalous contribution. The spectra of anomalous dimension is given in terms of the Lorentz invariant quadratic invariant (compact mass operator) of a conformal generator R μ with pure discrete spectrum. The perturbative reading of R o as a Hamiltonian in its own right, associated with an action in a functional integral setting naturally leads to the Ad S formulation. The formal service role of Ad S in order to access C QFT by a standard perturbative formalism (without being forced to understand first massive theories and then taking their scale-invariant limit) vastly increases the realm of conventionally accessible 4-dim. C QFT beyond those for which one had to use Lagrangians with supersymmetry in order to have a vanishing Beta-function. (author)

Calculations of the electronic levels, spin-Hamiltonian parameters and vibrational spectra for the CrCl{sub 3} layered crystals

Energy Technology Data Exchange (ETDEWEB)

Avram, C.N. [Faculty of Physics, West University of Timisoara, Bd. V. Parvan No. 4, 300223 Timisoara (Romania); Gruia, A.S., E-mail: adigruia@yahoo.com [Faculty of Physics, West University of Timisoara, Bd. V. Parvan No. 4, 300223 Timisoara (Romania); Brik, M.G. [College of Sciences, Chongqing University of Posts and Telecommunications, Chongqing 400065 (China); Institute of Physics, University of Tartu, Ravila 14C, Tartu 50411 (Estonia); Institute of Physics, Jan Dlugosz University, Armii Krajowej 13/15, PL-42200 Czestochowa (Poland); Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw (Poland); Barb, A.M. [Faculty of Physics, West University of Timisoara, Bd. V. Parvan No. 4, 300223 Timisoara (Romania)

2015-12-01

Calculations of the Cr{sup 3+} energy levels, spin-Hamiltonian parameters and vibrational spectra for the layered CrCl{sub 3} crystals are reported for the first time. The crystal field parameters and the energy level scheme were calculated in the framework of the Exchange Charge Model of crystal field. The spin-Hamiltonian parameters (zero-field splitting parameter D and g-factors) for Cr{sup 3+} ion in CrCl{sub 3} crystals were obtained using two independent techniques: i) semi-empirical crystal field theory and ii) density functional theory (DFT)-based model. In the first approach, the spin-Hamiltonian parameters were calculated from the perturbation theory method and the complete diagonalization (of energy matrix) method. The infrared (IR) and Raman frequencies were calculated for both experimental and fully optimized geometry of the crystal structure, using CRYSTAL09 software. The obtained results are discussed and compared with the experimental available data.

Non-integrability of the Armbruster-Guckenheimer-Kim quartic Hamiltonian through Morales-Ramis theory

OpenAIRE

Acosta-Humánez, P.; Alvarez-Ramírez, M.; Stuchi, T.

2017-01-01

We show the non-integrability of the three-parameter Armburster-Guckenheimer-Kim quartic Hamiltonian using Morales-Ramis theory, with the exception of the three already known integrable cases. We use Poincar\\'e sections to illustrate the breakdown of regular motion for some parameter values.

Extended hamiltonian formalism and Lorentz-violating lagrangians

Directory of Open Access Journals (Sweden)

Don Colladay

2017-09-01

Full Text Available A new perspective on the classical mechanical formulation of particle trajectories in Lorentz-violating theories is presented. Using the extended hamiltonian formalism, a Legendre Transformation between the associated covariant lagrangian and hamiltonian varieties is constructed. This approach enables calculation of trajectories using Hamilton's equations in momentum space and the Euler–Lagrange equations in velocity space away from certain singular points that arise in the theory. Singular points are naturally de-singularized by requiring the trajectories to be smooth functions of both velocity and momentum variables. In addition, it is possible to identify specific sheets of the dispersion relations that correspond to specific solutions for the lagrangian. Examples corresponding to bipartite Finsler functions are computed in detail. A direct connection between the lagrangians and the field-theoretic solutions to the Dirac equation is also established for a special case.

Extended hamiltonian formalism and Lorentz-violating lagrangians

Science.gov (United States)

Colladay, Don

2017-09-01

A new perspective on the classical mechanical formulation of particle trajectories in Lorentz-violating theories is presented. Using the extended hamiltonian formalism, a Legendre Transformation between the associated covariant lagrangian and hamiltonian varieties is constructed. This approach enables calculation of trajectories using Hamilton's equations in momentum space and the Euler-Lagrange equations in velocity space away from certain singular points that arise in the theory. Singular points are naturally de-singularized by requiring the trajectories to be smooth functions of both velocity and momentum variables. In addition, it is possible to identify specific sheets of the dispersion relations that correspond to specific solutions for the lagrangian. Examples corresponding to bipartite Finsler functions are computed in detail. A direct connection between the lagrangians and the field-theoretic solutions to the Dirac equation is also established for a special case.

Consistency of the Hamiltonian formulation of the lowest-order effective action of the complete Horava theory

International Nuclear Information System (INIS)

Bellorin, Jorge; Restuccia, Alvaro

2011-01-01

We perform the Hamiltonian analysis for the lowest-order effective action, up to second order in derivatives, of the complete Horava theory. The model includes the invariant terms that depend on ∂ i lnN proposed by Blas, Pujolas, and Sibiryakov. We show that the algebra of constraints closes. The Hamiltonian constraint is of second-class behavior and it can be regarded as an elliptic partial differential equation for N. The linearized version of this equation is a Poisson equation for N that can be solved consistently. The preservation in time of the Hamiltonian constraint yields an equation that can be consistently solved for a Lagrange multiplier of the theory. The model has six propagating degrees of freedom in the phase space, corresponding to three even physical modes. When compared with the λR model studied by us in a previous paper, it lacks two second-class constraints, which leads to the extra even mode.

Lifting particle coordinate changes of magnetic moment type to Vlasov-Maxwell Hamiltonian dynamics

International Nuclear Information System (INIS)

Morrison, P. J.; Vittot, M.; Guillebon, L. de

2013-01-01

Techniques for coordinate changes that depend on both dependent and independent variables are developed and applied to the Maxwell-Vlasov Hamiltonian theory. Particle coordinate changes with a new velocity variable dependent on the magnetic field, with spatial coordinates unchanged, are lifted to the field theoretic level, by transforming the noncanonical Poisson bracket and Hamiltonian structure of the Vlasov-Maxwell dynamics. Several examples are given including magnetic coordinates, where the velocity is decomposed into components parallel and perpendicular to the local magnetic field, and the case of spherical velocity coordinates. An example of the lifting procedure is performed to obtain a simplified version of gyrokinetics, where the magnetic moment is used as a coordinate and the dynamics is reduced by elimination of the electric field energy in the Hamiltonian.

Nonautonomous linear Hamiltonian systems oscillation, spectral theory and control

CERN Document Server

Johnson, Russell; Novo, Sylvia; Núñez, Carmen; Fabbri, Roberta

2016-01-01

This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is given to the oscillation properties of the solutions as well as to a spectral theory appropriate for such systems. The book contains extensions of results which are well known when the coefficients are autonomous or periodic, as well as in the nonautonomous two-dimensional case. However, a substantial part of the theory presented here is new even in those much simpler situations. The authors make systematic use of basic facts concerning Lagrange planes and symplectic matrices, and apply some fundamental methods of topological dynamics and ergodic theory. Among the tools used in the analysis, which include Lyapunov exponents, Weyl matrices, exponential dichotomy, and weak disconjugacy, a fundamental role is played by the rotation number for linear Hami...

A partial Hamiltonian approach for current value Hamiltonian systems

Science.gov (United States)

Naz, R.; Mahomed, F. M.; Chaudhry, Azam

2014-10-01

We develop a partial Hamiltonian framework to obtain reductions and closed-form solutions via first integrals of current value Hamiltonian systems of ordinary differential equations (ODEs). The approach is algorithmic and applies to many state and costate variables of the current value Hamiltonian. However, we apply the method to models with one control, one state and one costate variable to illustrate its effectiveness. The current value Hamiltonian systems arise in economic growth theory and other economic models. We explain our approach with the help of a simple illustrative example and then apply it to two widely used economic growth models: the Ramsey model with a constant relative risk aversion (CRRA) utility function and Cobb Douglas technology and a one-sector AK model of endogenous growth are considered. We show that our newly developed systematic approach can be used to deduce results given in the literature and also to find new solutions.

Functionals Hartree-Fock equations in the Schrodinger representation of quantum field theory

International Nuclear Information System (INIS)

Gamboa, J.

1989-08-01

Hartree-Fock equations for a scalar field theory in the Schrodinger representation are derived. It is shown that renormalization of the total energy in the functional Schrodinger equation is enterely contained in the eigenvalues of the Hartree-Fock hamiltonian. (A.C.A.S.) [pt

Lagrangian-Hamiltonian unified formalism for autonomous higher order dynamical systems

International Nuclear Information System (INIS)

Prieto-Martinez, Pedro Daniel; Roman-Roy, Narciso

2011-01-01

The Lagrangian-Hamiltonian unified formalism of Skinner and Rusk was originally stated for autonomous dynamical systems in classical mechanics. It has been generalized for non-autonomous first-order mechanical systems, as well as for first-order and higher order field theories. However, a complete generalization to higher order mechanical systems is yet to be described. In this work, after reviewing the natural geometrical setting and the Lagrangian and Hamiltonian formalisms for higher order autonomous mechanical systems, we develop a complete generalization of the Lagrangian-Hamiltonian unified formalism for these kinds of systems, and we use it to analyze some physical models from this new point of view. (paper)

The Electromagnetic Dipole Radiation Field through the Hamiltonian Approach

Science.gov (United States)

Likar, A.; Razpet, N.

2009-01-01

The dipole radiation from an oscillating charge is treated using the Hamiltonian approach to electrodynamics where the concept of cavity modes plays a central role. We show that the calculation of the radiation field can be obtained in a closed form within this approach by emphasizing the role of coherence between the cavity modes, which is…

Hamiltonian reductions in plasma physics about intrinsic gyrokinetic

International Nuclear Information System (INIS)

Guillebon de Resnes, L. de

2013-01-01

Gyrokinetic is a key model for plasma micro-turbulence, commonly used for fusion plasmas or small-scale astrophysical turbulence, for instance. The model still suffers from several issues, which could imply to reconsider the equations. This thesis dissertation clarifies three of them. First, one of the coordinates caused questions, both from a physical and from a mathematical point of view; a suitable constrained coordinate is introduced, which removes the issues from the theory and explains the intrinsic structures underlying the questions. Second, the perturbative coordinate transformation for gyrokinetic was computed only at lowest orders; explicit induction relations are obtained to go arbitrary order in the expansion. Third, the introduction of the coupling between the plasma and the electromagnetic field was not completely satisfactory; using the Hamiltonian structure of the dynamics, it is implemented in a more appropriate way, with strong consequences on the gyrokinetic equations, especially about their Hamiltonian structure. In order to address these three main points, several other results are obtained, for instance about the origin of the guiding-center adiabatic invariant, about a very efficient minimal guiding center transformation, or about an intermediate Hamiltonian model between Vlasov-Maxwell and gyrokinetic, where the characteristics include both the slow guiding-center dynamics and the fast gyro-angle dynamics. In addition, various reduction methods are used, introduced or developed, e.g. a Lie-transform of the equations of motion, a lifting method to transfer particle reductions to the corresponding Hamiltonian field dynamics, or a truncation method related both to Dirac's theory of constraints and to a projection onto a Lie-subalgebra. Besides gyrokinetic, this is useful to clarify other Hamiltonian reductions in plasma physics, for instance for incompressible or electrostatic dynamics, for magnetohydrodynamics, or for fluid closures including

Multichain Mean-Field Theory of Quasi-One-Dimensional Quantum Spin Systems

International Nuclear Information System (INIS)

Sandvik, A.W.

1999-01-01

A multichain mean-field theory is developed and applied to a two-dimensional system of weakly coupled S=1/2 Heisenberg chains. The environment of a chain C 0 is modeled by a number of neighboring chains C δ , δ=±1, hor-ellipsis,± , with the edge chains C ±n coupled to a staggered field. Using a quantum Monte Carlo method, the effective (2n+1) -chain Hamiltonian is solved self-consistently for n up to 4 . The results are compared with simulation results for the original Hamiltonian on large rectangular lattices. Both methods show that the staggered magnetization M for small interchain couplings α behaves as M∼√(α) enhanced by a multiplicative logarithmic correction. copyright 1999 The American Physical Society

Symplectic and Hamiltonian structures of nonlinear evolution equations

International Nuclear Information System (INIS)

Dorfman, I.Y.

1993-01-01

A Hamiltonian structure on a finite-dimensional manifold can be introduced either by endowing it with a (pre)symplectic structure, or by describing the Poisson bracket with the help of a tensor with two upper indices named the Poisson structure. Under the assumption of nondegeneracy, the Poisson structure is nothing else than the inverse of the symplectic structure. Also in the degenerate case the distinction between the two approaches is almost insignificant, because both presymplectic and Poisson structures split into symplectic structures on leaves of appropriately chosen foliations. Hamiltonian structures that arise in the theory of evolution equations demonstrate something new in this respect: trying to operate in local terms, one is induced to develop both approaches independently. Hamiltonian operators, being the infinite-dimensional counterparts of Poisson structures, were the first to become the subject of investigations. A considerable period of time passed before the papers initiated research in the theory of symplectic operators, being the counterparts of presymplectic structures. In what follows, we focus on the main achievements in this field

Towards a coupled-cluster treatment of SU(N) lattice gauge field theory

NARCIS (Netherlands)

Bishop, Raymond F.; Ligterink, N.E.; Walet, Niels R.

2006-01-01

A consistent approach to Hamiltonian SU(N) lattice gauge field theory is developed using the maximal-tree gauge and an appropriately chosen set of angular variables. The various constraints are carefully discussed, as is a practical means for their implementation. A complete set of variables for the

Fluctuations around classical solutions for gauge theories in Lagrangian and Hamiltonian approach

International Nuclear Information System (INIS)

Miskovic, Olivera; Pons, Josep M

2006-01-01

We analyse the dynamics of gauge theories and constrained systems in general under small perturbations around a classical solution in both Lagrangian and Hamiltonian formalisms. We prove that a fluctuations theory, described by a quadratic Lagrangian, has the same constraint structure and number of physical degrees of freedom as the original non-perturbed theory, assuming the non-degenerate solution has been chosen. We show that the number of Noether gauge symmetries is the same in both theories, but that the gauge algebra in the fluctuations theory becomes Abelianized. We also show that the fluctuations theory inherits all functionally independent rigid symmetries from the original theory and that these symmetries are generated by linear or quadratic generators according to whether the original symmetry is preserved by the background or is broken by it. We illustrate these results with examples

Non-integrable quantum field theories as perturbations of certain integrable models

International Nuclear Information System (INIS)

Delfino, G.; Simonetti, P.

1996-03-01

We approach the study of non-integrable models of two-dimensional quantum field theory as perturbations of the integrable ones. By exploiting the knowledge of the exact S-matrix and Form Factors of the integrable field theories we obtain the first order corrections to the mass ratios, the vacuum energy density and the S-matrix of the non-integrable theories. As interesting applications of the formalism, we study the scaling region of the Ising model in an external magnetic field at T ∼ T c and the scaling region around the minimal model M 2 , τ . For these models, a remarkable agreement is observed between the theoretical predictions and the data extracted by a numerical diagonalization of their Hamiltonian. (author). 41 refs, 9 figs, 1 tab

Effective field theory approach to structure functions at small xBj

International Nuclear Information System (INIS)

Nachtmann, O.

2003-01-01

We relate the structure functions of deep inelastic lepton-nucleon scattering to current-current correlation functions in a Euclidean field theory depending on a parameter r. The r-dependent Hamiltonian of the theory is P 0 -(1-r)P 3 , with P 0 the usual Hamiltonian and P 3 the third component of the momentum operator. We show that a small x Bj in the structure functions corresponds to the small r limit of the effective theory. We argue that for r→0 there is a critical regime of the theory where simple scaling relations should hold. We show that in this framework Regge behaviour of the structure functions obtained with the hard pomeron ansatz corresponds to a scaling behaviour of the matrix elements in the effective theory where the intercept of the hard pomeron appears as a critical index. Explicit expressions for various analytic continuations of the structure functions and matrix elements are given as well as path integral representations for the matrix elements in the effective theory. Our aim is to provide a framework for truly non-perturbative calculations of the structure functions at small x Bj for arbitrary Q 2 . (orig.)

Existence for stationary mean-field games with congestion and quadratic Hamiltonians

KAUST Repository

Gomes, Diogo A.; Mitake, Hiroyoshi

2015-01-01

Here, we investigate the existence of solutions to a stationary mean-field game model introduced by J.-M. Lasry and P.-L. Lions. This model features a quadratic Hamiltonian and congestion effects. The fundamental difficulty of potential singular

Asymmetric Invisibility Cloaking Theory Based on the Concept of Effective Electromagnetic Fields for Photons

Science.gov (United States)

Amemiya, Tomo; Taki, Masato; Kanazawa, Toru; Arai, Shigehisa

2014-03-01

The asymmetric invisibility cloak is a special cloak with unidirectional transparency; that is, a person in the cloak should not be seen from the outside but should be able to see the outside. Existing theories of designing invisibility cloaks cannot be used for asymmetric cloaking because they are based on the transformation optics that uses Riemannian metric tensor independent of direction. To overcome this problem, we propose introducing directionality into invisibility cloaking. Our theory is based on ``the theory of effective magnetic field for photons'' proposed by Stanford University.[2] To realize asymmetric cloaking, we have extended the Stanford's theory to add the concept of ``effective electric field for photons.'' The effective electric and the magnetic field can be generated using a photonc resonator lattice, which is a kind of metamaterial. The Hamiltonian for photons in these fields has a similar form to that of the Hamiltonian for a charged particle in an electromagnetic field. An incident photon therefore experiences a ``Lorentz-like'' and a ``Coulomb-like'' force and shows asymmetric movement depending of its travelling direction.We show the procedure of designing actual invisibility cloaks using the photonc resonator lattice and confirm their operation with the aid of computer simulation. This work was supported in part by the MEXT; JSPS KAKENHI Grant Numbers #24246061, #24656046, #25420321, #25420322.

Sine-square deformation of solvable spin chains and conformal field theories

International Nuclear Information System (INIS)

Katsura, Hosho

2012-01-01

We study solvable spin chains, one-dimensional massless Dirac fermions and conformal field theories (CFTs) with sine-square deformation (SSD), in which the Hamiltonian density is modulated by the function f(x) = sin  2 (πx/ℓ), where x is the position and ℓ is the length of the system. For the XY chain and the transverse field Ising chain at criticality, it is shown that the ground state of an open system with SSD is identical to that of a uniform chain with periodic boundary conditions. The same holds for the massless Dirac fermions with SSD, corresponding to the continuum limit of the gapless XY chain. For general CFTs, we find that the Hamiltonian of a system with SSD has an expression in terms of the generators of the Virasoro algebra. This allows us to show that the vacuum state is an exact eigenstate of the sine-square deformed Hamiltonian. Furthermore, for a restricted class of CFTs associated with affine Lie (Kac–Moody) algebras, including c = 1 Gaussian CFT, we prove that the vacuum is an exact ground state of the deformed Hamiltonian. This explains why the SSD has succeeded in suppressing boundary effects in one-dimensional critical systems, as observed in previous numerical studies. (paper)

Fractional Hamiltonian analysis of higher order derivatives systems

International Nuclear Information System (INIS)

Baleanu, Dumitru; Muslih, Sami I.; Tas, Kenan

2006-01-01

The fractional Hamiltonian analysis of 1+1 dimensional field theory is investigated and the fractional Ostrogradski's formulation is obtained. The fractional path integral of both simple harmonic oscillator with an acceleration-squares part and a damped oscillator are analyzed. The classical results are obtained when fractional derivatives are replaced with the integer order derivatives

Superstring field theory

International Nuclear Information System (INIS)

Green, M.B.

1984-01-01

Superstring field theories are formulated in terms of light-cone-gauge superfields that are functionals of string coordinates chi(sigma) and theta(sigma). The formalism used preserves only the manifest SU(4) symmetry that corresponds to rotations among six of the eight transverse directions. In type I theories, which have one ten-dimensional supersymmetry and describe both open and closed strings, there are five interaction terms of two basic kinds. One kind is a breaking or joining interaction, which is a string generalization of a cubic Yang-Mills coupling. It is relevant to both the three open-string vertex and the open-string to closed-string transition vertex. The other kind is an exchange or crossing-over interaction, which is a string generalization of a cubic gravitational coupling. All the interactions can be uniquely determined by requiring continuity of the coordinates chi(sigma) and theta(sigma) (which implies local conservation of the conjugate momenta) and by imposing the global supersymmetry algebra. Specific local operators are identified for each of the two kinds of interactions. In type II theories, which have two ten-dimensional supersymmetries and contain closed strings only, the entire interaction hamiltonian consists of a single cubic vertex. The higher-order contact terms of the N=8 supergravity theory that arises in the low-energy limit give an effective description of the exchange of massive string modes. (orig.)

Field theory methods applied for the study of superconductivity in one-dimensional systems

International Nuclear Information System (INIS)

Martins, M.J.

1986-01-01

It is shown that the Froehlich's hamiltonian in one spatial dimension is identical to that of an exactly solvable field Theory. The spectrum of the theory is computed. A critical coupling is found above which the system becomes unstable, indicating a superconducting transition. It is also proposed and investigated a renormalizable relativistic field theory model in two space-time dimensions, with quartic self-interaction among N species of fermions, which undergoes dynamical generation of a superconducting gap and is asymptotically free. A finite temperature is introduced and, for N -> ∞ a critical value T c is found above which the gap vanishes. (author)

Lennard-Jones triple-point bulk and shear viscosities. Green-Kubo theory, Hamiltonian mechanics, and nonequilibrium molecular dynamics

International Nuclear Information System (INIS)

Hoover, W.G.; Evans, D.J.; Hickman, R.B.; Ladd, A.J.C.; Ashurst, W.T.; Moran, B.

1980-01-01

A new Hamiltonian method for deformation simulations is related to the Green-Kubo fluctuation theory through perturbation theory and linear-response theory. Numerical results for the bulk and shear viscosity coefficients are compared to corresponding Green-Kubo calculations. Both viscosity coefficients depend similarly on frequency, in a way consistent with enhanced ''long-time tails.''

The Closed-Orbit Theory for General Rydberg Atoms in External Fields

International Nuclear Information System (INIS)

Carboni, R.

1997-01-01

The photoabsorption spectra of hydrogen Rydberg atoms, as well of model Rydberg atoms in pure magnetic or electric fields have been successfully calculated using the semiclassical closed-orbit theory. The theory relates the resonances of the spectra to closed classical orbits of the excited electron. The dynamics of multielectron atoms is more complicated than the hydrogenic one; additionally, when the atoms are in the presence of perpendicular magnetic and electric fields becomes more complex than when they are in pure fields, due to the fact that the Hamiltonian is non-separable in three degrees of freedom, instead of two non-separable degrees of freedom. In this work, I present an extension of the closed-orbit theory to three degrees of freedom, considering arbitrary quantum defects, i.e., general atoms. (Author) [es

QCD unitarity constraints on Reggeon Field Theory

Energy Technology Data Exchange (ETDEWEB)

Kovner, Alex [Physics Department, University of Connecticut,2152 Hillside Road, Storrs, CT 06269 (United States); Levin, Eugene [Departemento de Física, Universidad Técnica Federico Santa María,and Centro Científico-Tecnológico de Valparaíso,Avda. Espana 1680, Casilla 110-V, Valparaíso (Chile); Department of Particle Physics, Tel Aviv University,Tel Aviv 69978 (Israel); Lublinsky, Michael [Physics Department, Ben-Gurion University of the Negev,Beer Sheva 84105 (Israel); Physics Department, University of Connecticut,2152 Hillside Road, Storrs, CT 06269 (United States)

2016-08-04

We point out that the s-channel unitarity of QCD imposes meaningful constraints on a possible form of the QCD Reggeon Field Theory. We show that neither the BFKL nor JIMWLK nor Braun’s Hamiltonian satisfy the said constraints. In a toy, zero transverse dimensional case we construct a model that satisfies the analogous constraint and show that at infinite energy it indeed tends to a “black disk limit' as opposed to the model with triple Pomeron vertex only, routinely used as a toy model in the literature.

QCD unitarity constraints on Reggeon Field Theory

International Nuclear Information System (INIS)

Kovner, Alex; Levin, Eugene; Lublinsky, Michael

2016-01-01

We point out that the s-channel unitarity of QCD imposes meaningful constraints on a possible form of the QCD Reggeon Field Theory. We show that neither the BFKL nor JIMWLK nor Braun’s Hamiltonian satisfy the said constraints. In a toy, zero transverse dimensional case we construct a model that satisfies the analogous constraint and show that at infinite energy it indeed tends to a “black disk limit' as opposed to the model with triple Pomeron vertex only, routinely used as a toy model in the literature.

Hamiltonian Dynamics and Positive Energy in General Relativity

Energy Technology Data Exchange (ETDEWEB)

Deser, S. [Physics Department, Brandeis University, Waltham, MA (United States)

1969-07-15

A review is first given of the Hamiltonian formulation of general relativity; the gravitational field is a self-interacting massless spin-two system within the framework of ordinary Lorentz covariant field theory. The recently solved problem of positive-definiteness of the field energy is then discussed. The latter, a conserved functional of the dynamical variables, is shown to have only one extremum, a local minimum, which is the vacuum state (flat space). This implies positive energy for the field, with the vacuum as ground-state. Similar results hold when minimally coupled matter is present. (author)

ON HAMILTONIAN FORMULATIONS AND CONSERVATION LAWS FOR PLATE THEORIES OF VEKUA-AMOSOV TYPE

Directory of Open Access Journals (Sweden)

Sergey I. Zhavoronok

2017-12-01

Full Text Available Some variants of the generalized Hamiltonian formulation of the plate theory of I. N. Vekua – A. A. Amosov type are presented. The infinite dimensional formulation with one evolution variable, or an “instantaneous” formalism, as well as the de Donder – Weyl one are considered, and their application to the numerical simulation of shell and plate dynamics is briefly discussed. The main conservation laws are formulated for the general plate theory of Nth order, and the possible motion integrals are introduced

Non-perturbative analysis of some simple field theories on a momentum space lattice

International Nuclear Information System (INIS)

Brooks, E.D. III.

1984-01-01

In this work, a new technique is developed for the numerical study of quantum field theory. The procedure, borrowed from nonrelativistic quantum mechanics, is that of finding the eigenvalues of a finite Hamiltonian matrix. The matrix is created by evaluating the matrix elements of the Hamiltonian operator on a finite basis of states. The eigenvalues and eigenvectors of the finite dimensional matrix become an accurate approximation to those of the physical system as the finite basis of states is extended to become more complete. A model of scalars coupled to fermions in 0 + 1 dimensions as a simple field theory is studied to consider in the course of developing the technique. Having developed the numerical and analytical techniques, a Fermi field coupled to a Bose field in 1 + 1 dimensions with the Yukawa coupling lambda anti-psi phi psi is considered. The large coupling limit basis of the 0 + 1 dimensional model is extended to this case using a Bogoliubov transformation on the fermions. It provides a handle on the behavior of the system in the large coupling limit. The effects of renormalization and the generation of bound states are considered

Energy-momentum tensor in the quantum field theory

International Nuclear Information System (INIS)

Azakov, S.I.

1977-01-01

An energy-momentum tensor in the scalar field theory is built. The tensor must satisfy the finiteness requirement of the Green function. The Green functions can always be made finite by renormalizations in the S-matrix by introducing counter terms into the Hamiltonian (or Lagrangian) of the interaction. Such a renormalization leads to divergencies in the Green functions. Elimination of these divergencies requires the introduction of new counter terms, which must be taken into account in the energy-momentum tensor

Quantum mean-field theory of collective dynamics and tunneling

International Nuclear Information System (INIS)

Negele, J.W.

1981-01-01

A fundamental problem in quantum many-body theory is formulation of a microscopic theory of collective motion. For self-bound, saturating systems like finite nuclei described in the context of nonrelativistic quantum mechanics with static interactions, the essential problem is how to formulate a systematic quantal theory in which the relevant collective variables and their dynamics arise directly and naturally from the Hamiltonian and the system under consideration. Significant progress has been made recently in formulating the quantum many-body problem in terms of an expansion about solutions to time-dependent mean-field equations. The essential ideas, principal results, and illustrative examples are summarized. An exact expression for an observable of interest is written using a functional integral representation for the evolution operator, and tractable time-dependent mean field equations are obtained by application of the stationary-phase approximation (SPA) to the functional integral. Corrections to the lowest-order theory may be systematically enumerated. 6 figures

How to quantize supersymmetric theories

International Nuclear Information System (INIS)

Smilga, A.V.

1985-01-01

A recipe for resolving the ordering ambiguities in quantum hamiltonians of supersymmetric theories is suggested. The Weyl ordering procedure applied to classical supercharges expressed as functions on the phase space of a classically supersymmetric system is shown to result in quantum operators which satisfy usual SUSY algebra. The quantum hamiltonian does not always coincide with the Weyl ordered classical hamiltonian function. The difference is due to that the Weyl symbol of the supercharge anticommutator does not coincide with the Poisson bracket of their Weyl symbols (i.e. the classical hamiltonian). The procedure is applied to supersymmetric σ-models (both N=2 and N=1 cases are analyzed) and also to the supersymmetric SU(2) Yang-Mills theory. Only quantum mechanical systems following from field theories when fields are assumed to be independent of space coordinates are considered. For gauge theories thesuggested recipe for quantization leads to the same result as the well-known Dirac recipe

Hamiltonian analysis of curvature-squared gravity with or without conformal invariance

Science.gov (United States)

KlusoÅ, Josef; Oksanen, Markku; Tureanu, Anca

2014-03-01

We analyze gravitational theories with quadratic curvature terms, including the case of conformally invariant Weyl gravity, motivated by the intention to find a renormalizable theory of gravity in the ultraviolet region, yet yielding general relativity at long distances. In the Hamiltonian formulation of Weyl gravity, the number of local constraints is equal to the number of unstable directions in phase space, which in principle could be sufficient for eliminating the unstable degrees of freedom in the full nonlinear theory. All the other theories of quadratic type are unstable—a problem appearing as ghost modes in the linearized theory. We find that the full projection of the Weyl tensor onto a three-dimensional hypersurface contains an additional fully traceless component, given by a quadratic extrinsic curvature tensor. A certain inconsistency in the literature is found and resolved: when the conformal invariance of Weyl gravity is broken by a cosmological constant term, the theory becomes pathological, since a constraint required by the Hamiltonian analysis imposes the determinant of the metric of spacetime to be zero. In order to resolve this problem by restoring the conformal invariance, we introduce a new scalar field that couples to the curvature of spacetime, reminiscent of the introduction of vector fields for ensuring the gauge invariance.

Next-to-next-to-leading order gravitational spin-orbit coupling via the effective field theory for spinning objects in the post-Newtonian scheme

Energy Technology Data Exchange (ETDEWEB)

Levi, Michele [Université Pierre et Marie Curie, CNRS-UMR 7095, Institut d' Astrophysique de Paris, 98 bis Boulevard Arago, 75014 Paris (France); Steinhoff, Jan, E-mail: michele.levi@upmc.fr, E-mail: jan.steinhoff@aei.mpg.de [Max-Planck-Institute for Gravitational Physics (Albert-Einstein-Institute), Am Mühlenberg 1, 14476 Potsdam-Golm (Germany)

2016-01-01

We implement the effective field theory for gravitating spinning objects in the post-Newtonian scheme at the next-to-next-to-leading order level to derive the gravitational spin-orbit interaction potential at the third and a half post-Newtonian order for rapidly rotating compact objects. From the next-to-next-to-leading order interaction potential, which we obtain here in a Lagrangian form for the first time, we derive straightforwardly the corresponding Hamiltonian. The spin-orbit sector constitutes the most elaborate spin dependent sector at each order, and accordingly we encounter a proliferation of the relevant Feynman diagrams, and a significant increase of the computational complexity. We present in detail the evaluation of the interaction potential, going over all contributing Feynman diagrams. The computation is carried out in terms of the ''nonrelativistic gravitational'' fields, which are advantageous also in spin dependent sectors, together with the various gauge choices included in the effective field theory for gravitating spinning objects, which also optimize the calculation. In addition, we automatize the effective field theory computations, and carry out the automated computations in parallel. Such automated effective field theory computations would be most useful to obtain higher order post-Newtonian corrections. We compare our Hamiltonian to the ADM Hamiltonian, and arrive at a complete agreement between the ADM and effective field theory results. Finally, we provide Hamiltonians in the center of mass frame, and complete gauge invariant relations among the binding energy, angular momentum, and orbital frequency of an inspiralling binary with generic compact spinning components to third and a half post-Newtonian order. The derivation presented here is essential to obtain further higher order post-Newtonian corrections, and to reach the accuracy level required for the successful detection of gravitational radiation.

Entanglement hamiltonian and entanglement contour in inhomogeneous 1D critical systems

Science.gov (United States)

Tonni, Erik; Rodríguez-Laguna, Javier; Sierra, Germán

2018-04-01

Inhomogeneous quantum critical systems in one spatial dimension have been studied by using conformal field theory in static curved backgrounds. Two interesting examples are the free fermion gas in the harmonic trap and the inhomogeneous XX spin chain called rainbow chain. For conformal field theories defined on static curved spacetimes characterised by a metric which is Weyl equivalent to the flat metric, with the Weyl factor depending only on the spatial coordinate, we study the entanglement hamiltonian and the entanglement spectrum of an interval adjacent to the boundary of a segment where the same boundary condition is imposed at the endpoints. A contour function for the entanglement entropies corresponding to this configuration is also considered, being closely related to the entanglement hamiltonian. The analytic expressions obtained by considering the curved spacetime which characterises the rainbow model have been checked against numerical data for the rainbow chain, finding an excellent agreement.

Hamiltonian formalism of the Skyrme model with ω mesons

International Nuclear Information System (INIS)

Adami, C.

1988-07-01

We have in this thesis presented the semiclassical quantum theory of the Skyrme model with coupling to an isoscalar gauge field. For the quantization of the classical theory we used the Hamiltonian formalism. Furthermore we have studied the consequences of the canonical treatment, whereby we found the explicite πN vertex of the theory, as well as presented the correct treatment of the spatial contribution of the ω field. Furthermore we indicated that a consistent treatment requires the summation of all tree diagrams of the theory with internal π and ω lines. Such a calculation contains the explicite construction of solutions for the coupled πω field equations. A further result of this thesis concerns the application of the linear πN vertex to the calculation of the Δ decay width via the process Δ→Nπ. (orig./HSI) [de

Bogoliubov transformations and fermion condensates in lattice field theories

International Nuclear Information System (INIS)

Caracciolo, Sergio; Palumbo, Fabrizio; Viola, Giovanni

2009-01-01

We apply generalized Bogoliubov transformations to the transfer matrix of relativistic field theories regularized on a lattice. We derive the conditions these transformations must satisfy to factorize the transfer matrix into two terms which propagate fermions and antifermions separately, and we solve the relative equations under some conditions. We relate these equations to the saddle point approximation of a recent bosonization method and to the Foldy-Wouthuysen transformations which separate positive from negative energy states in the Dirac Hamiltonian

Integrable Hamiltonian systems and spectral theory

CERN Document Server

Moser, J

1981-01-01

Classical integrable Hamiltonian systems and isospectral deformations ; geodesics on an ellipsoid and the mechanical system of C. Neumann ; the Schrödinger equation for almost periodic potentials ; finite band potentials ; limit cases, Bargmann potentials.

Almost periodic Hamiltonians: an algebraic approach

International Nuclear Information System (INIS)

Bellissard, J.

1981-07-01

We develop, by analogy with the study of periodic potential, an algebraic theory for almost periodic hamiltonians, leading to a generalized Bloch theorem. This gives rise to results concerning the spectral measures of these operators in terms of those of the corresponding Bloch hamiltonians

Renormalization of Hamiltonian QCD

International Nuclear Information System (INIS)

Andrasi, A.; Taylor, John C.

2009-01-01

We study to one-loop order the renormalization of QCD in the Coulomb gauge using the Hamiltonian formalism. Divergences occur which might require counter-terms outside the Hamiltonian formalism, but they can be cancelled by a redefinition of the Yang-Mills electric field.

On a kind of Noether symmetries and conservation laws in k-cosymplectic field theory

International Nuclear Information System (INIS)

Marrero, Juan Carlos; Roman-Roy, Narciso; Salgado, Modesto; Vilarino, Silvia

2011-01-01

This paper is devoted to studying symmetries of certain kinds of k-cosymplectic Hamiltonian systems in first-order classical field theories. Thus, we introduce a particular class of symmetries and study the problem of associating conservation laws to them by means of a suitable generalization of Noether's theorem.

Effective-field-theory model for the fractional quantum Hall effect

International Nuclear Information System (INIS)

Zhang, S.C.; Hansson, T.H.; Kivelson, S.

1989-01-01

Starting directly from the microscopic Hamiltonian, we derive a field-theory model for the fractional quantum hall effect. By considering an approximate coarse-grained version of the same model, we construct a Landau-Ginzburg theory similar to that of Girvin. The partition function of the model exhibits cusps as a function of density and the Hall conductance is quantized at filling factors ν = (2k-1)/sup -1/ with k an arbitrary integer. At these fractions the ground state is incompressible, and the quasiparticles and quasiholes have fractional charge and obey fractional statistics. Finally, we show that the collective density fluctuations are massive

Relativistic n-body wave equations in scalar quantum field theory

International Nuclear Information System (INIS)

Emami-Razavi, Mohsen

2006-01-01

The variational method in a reformulated Hamiltonian formalism of Quantum Field Theory (QFT) is used to derive relativistic n-body wave equations for scalar particles (bosons) interacting via a massive or massless mediating scalar field (the scalar Yukawa model). Simple Fock-space variational trial states are used to derive relativistic n-body wave equations. The equations are shown to have the Schroedinger non-relativistic limits, with Coulombic interparticle potentials in the case of a massless mediating field and Yukawa interparticle potentials in the case of a massive mediating field. Some examples of approximate ground state solutions of the n-body relativistic equations are obtained for various strengths of coupling, for both massive and massless mediating fields

BCS wave function, matrix product states, and the Ising conformal field theory

Science.gov (United States)

Montes, Sebastián; Rodríguez-Laguna, Javier; Sierra, Germán

2017-11-01

We present a characterization of the many-body lattice wave functions obtained from the conformal blocks (CBs) of the Ising conformal field theory (CFT). The formalism is interpreted as a matrix product state using continuous ancillary degrees of freedom. We provide analytic and numerical evidence that the resulting states can be written as BCS states. We give a complete proof that the translationally invariant 1D configurations have a BCS form and we find suitable parent Hamiltonians. In particular, we prove that the ground state of the finite-size critical Ising transverse field (ITF) Hamiltonian can be obtained with this construction. Finally, we study 2D configurations using an operator product expansion (OPE) approximation. We associate these states to the weak pairing phase of the p +i p superconductor via the scaling of the pairing function and the entanglement spectrum.

Time dependent drift Hamiltonian

International Nuclear Information System (INIS)

Boozer, A.H.

1982-04-01

The motion of individual charged particles in a given magnetic and an electric fields is discussed. An idea of a guiding center distribution function f is introduced. The guiding center distribution function is connected to the asymptotic Hamiltonian through the drift kinetic equation. The general non-stochastic magnetic field can be written in a contravariant and a covariant forms. The drift Hamiltonian is proposed, and the canonical gyroradius is presented. The proposed drift Hamiltonian agrees with Alfven's drift velocity to lowest non-vanishing order in the gyroradius. The relation between the exact, time dependent equations of motion and the guiding center equation is clarified by a Lagrangian analysis. The deduced Lagrangian represents the drift motion. (Kato, T.)

Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces

CERN Document Server

Jacob, Birgit

2012-01-01

This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results, then progresses smoothly to advanced topics in current research. Many physical systems can be formulated using a Hamiltonian framework, leading to models described by ordinary or partial differential equations. For the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take into account this interaction with the environment. This book is the fir

Extension of PT-symmetric quantum mechanics to quantum field theory with cubic interaction

International Nuclear Information System (INIS)

Bender, Carl M.; Brody, Dorje C.; Jones, Hugh F.

2004-01-01

It has recently been shown that a non-Hermitian Hamiltonian H possessing an unbroken PT symmetry (i) has a real spectrum that is bounded below, and (ii) defines a unitary theory of quantum mechanics with positive norm. The proof of unitarity requires a linear operator C, which was originally defined as a sum over the eigenfunctions of H. However, using this definition to calculate C is cumbersome in quantum mechanics and impossible in quantum field theory. An alternative method is devised here for calculating C directly in terms of the operator dynamical variables of the quantum theory. This method is general and applies to a variety of quantum mechanical systems having several degrees of freedom. More importantly, this method is used to calculate the C operator in quantum field theory. The C operator is a time-independent observable in PT-symmetric quantum field theory

Phase structure of (φ4)3 field theory at finite temperature

International Nuclear Information System (INIS)

Efimov, G.V.

1992-01-01

Phase structure of φ 4 field theory in the space-time R 3 is investigated at arbitrary coupling constant and temperature. The critical values of the coupling constant and temperature, corresponding to the phase transitions in the system, are calculated by the canonical transformation method within formalism of thermo field dynamics. The Hamiltonians describing the system in each phase are obtained straightforwardly. Comparison with the two-dimensional case shows a crucial influence of higher order renormalization on the phase structure of the model. 13 refs.; 5 figs

Polynomial Similarity Transformation Theory: A smooth interpolation between coupled cluster doubles and projected BCS applied to the reduced BCS Hamiltonian

Energy Technology Data Exchange (ETDEWEB)

Degroote, M. [Rice Univ., Houston, TX (United States); Henderson, T. M. [Rice Univ., Houston, TX (United States); Zhao, J. [Rice Univ., Houston, TX (United States); Dukelsky, J. [Consejo Superior de Investigaciones Cientificas (CSIC), Madrid (Spain). Inst. de Estructura de la Materia; Scuseria, G. E. [Rice Univ., Houston, TX (United States)

2018-01-03

We present a similarity transformation theory based on a polynomial form of a particle-hole pair excitation operator. In the weakly correlated limit, this polynomial becomes an exponential, leading to coupled cluster doubles. In the opposite strongly correlated limit, the polynomial becomes an extended Bessel expansion and yields the projected BCS wavefunction. In between, we interpolate using a single parameter. The e ective Hamiltonian is non-hermitian and this Polynomial Similarity Transformation Theory follows the philosophy of traditional coupled cluster, left projecting the transformed Hamiltonian onto subspaces of the Hilbert space in which the wave function variance is forced to be zero. Similarly, the interpolation parameter is obtained through minimizing the next residual in the projective hierarchy. We rationalize and demonstrate how and why coupled cluster doubles is ill suited to the strongly correlated limit whereas the Bessel expansion remains well behaved. The model provides accurate wave functions with energy errors that in its best variant are smaller than 1% across all interaction stengths. The numerical cost is polynomial in system size and the theory can be straightforwardly applied to any realistic Hamiltonian.

Light front field theory: an advanced primer

International Nuclear Information System (INIS)

Martinovic, L.

2007-01-01

We present an elementary introduction to quantum field theory formulated in terms of Dirac's light front variables. In addition to general principles and methods, a few more specific topics and approaches based on the author's work will be discussed. Most of the discussion deals with massive two-dimensional models formulated in a finite spatial volume starting with a detailed comparison between quantization of massive free fields in the usual field theory and the light front (LF) quantization. We discuss basic properties such as relativistic invariance and causality. After the LF treatment of the soluble Federbush model, a LF approach to spontaneous symmetry breaking is explained and a simple gauge theory - the massive Schwinger model in various gauges is studied. A LF version of bosonization and the massive Thirring model are also discussed. A special chapter is devoted to the method of discretized light cone quantization and its application to calculations of the properties of quantum solitons. The problem of LF zero modes is illustrated with the example of the two/dimensional Yukawa model. Hamiltonian perturbation theory in the LF formulation is derived and applied to a few simple processes to demonstrate its advantages. As a byproduct, it is shown that the LF theory cannot be obtained as a 'light-like' limit of the usual field theory quantized on a initial space-like surface. A simple LF formulation of the Higgs mechanism is then given Since our intention was to provide a treatment of the light front quantization accessible to postgradual students, an effort was made to discuss most of the topics pedagogically and number of technical details and derivations are contained in the appendices (Author)

Modular Hamiltonians on the null plane and the Markov property of the vacuum state

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Casini, Horacio; Testé, Eduardo; Torroba, Gonzalo

2017-09-01

We compute the modular Hamiltonians of regions having the future horizon lying on a null plane. For a CFT this is equivalent to regions with a boundary of arbitrary shape lying on the null cone. These Hamiltonians have a local expression on the horizon formed by integrals of the stress tensor. We prove this result in two different ways, and show that the modular Hamiltonians of these regions form an infinite dimensional Lie algebra. The corresponding group of unitary transformations moves the fields on the null surface locally along the null generators with arbitrary null line dependent velocities, but act non-locally outside the null plane. We regain this result in greater generality using more abstract tools on the algebraic quantum field theory. Finally, we show that modular Hamiltonians on the null surface satisfy a Markov property that leads to the saturation of the strong sub-additive inequality for the entropies and to the strong super-additivity of the relative entropy.

Electrostatics of proteins in dielectric solvent continua. II. Hamiltonian reaction field dynamics

Energy Technology Data Exchange (ETDEWEB)

Bauer, Sebastian; Tavan, Paul; Mathias, Gerald, E-mail: gerald.mathias@physik.uni-muenchen.de [Lehrstuhl für BioMolekulare Optik, Ludig-Maximilians Universität München, Oettingenstr. 67, 80538 München (Germany)

2014-03-14

In Paper I of this work [S. Bauer, G. Mathias, and P. Tavan, J. Chem. Phys. 140, 104102 (2014)] we have presented a reaction field (RF) method, which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of polarizable molecular mechanics (MM) force fields. Building upon these results, here we suggest a method for linearly scaling Hamiltonian RF/MM molecular dynamics (MD) simulations, which we call “Hamiltonian dielectric solvent” (HADES). First, we derive analytical expressions for the RF forces acting on the solute atoms. These forces properly account for all those conditions, which have to be self-consistently fulfilled by RF quantities introduced in Paper I. Next we provide details on the implementation, i.e., we show how our RF approach is combined with a fast multipole method and how the self-consistency iterations are accelerated by the use of the so-called direct inversion in the iterative subspace. Finally we demonstrate that the method and its implementation enable Hamiltonian, i.e., energy and momentum conserving HADES-MD, and compare in a sample application on Ac-Ala-NHMe the HADES-MD free energy landscape at 300 K with that obtained in Paper I by scanning of configurations and with one obtained from an explicit solvent simulation.

Generalized quantum sine-Gordon equation and its relation to the Thirring model in quantum field theory

International Nuclear Information System (INIS)

Skagerstam, B.K.

1976-01-01

We discuss a generalization of the conventional sine-Gordon quantum field theory by using methods recently developed by Coleman. As a result we can argue that the equivalence between the sine-Gordon theory and the massive Thirring model is unaffected if we perturb the sine-Gordon Hamiltonian by a bounded perturbation consisting of a continuous sum of sine-Gordon type interactions

Can model Hamiltonians describe the electron–electron interaction in π-conjugated systems?: PAH and graphene

International Nuclear Information System (INIS)

Chiappe, G; Louis, E; San-Fabián, E; Vergés, J A

2015-01-01

Model Hamiltonians have been, and still are, a valuable tool for investigating the electronic structure of systems for which mean field theories work poorly. This review will concentrate on the application of Pariser–Parr–Pople (PPP) and Hubbard Hamiltonians to investigate some relevant properties of polycyclic aromatic hydrocarbons (PAH) and graphene. When presenting these two Hamiltonians we will resort to second quantisation which, although not the way chosen in its original proposal of the former, is much clearer. We will not attempt to be comprehensive, but rather our objective will be to try to provide the reader with information on what kinds of problems they will encounter and what tools they will need to solve them. One of the key issues concerning model Hamiltonians that will be treated in detail is the choice of model parameters. Although model Hamiltonians reduce the complexity of the original Hamiltonian, they cannot be solved in most cases exactly. So, we shall first consider the Hartree–Fock approximation, still the only tool for handling large systems, besides density functional theory (DFT) approaches. We proceed by discussing to what extent one may exactly solve model Hamiltonians and the Lanczos approach. We shall describe the configuration interaction (CI) method, a common technology in quantum chemistry but one rarely used to solve model Hamiltonians. In particular, we propose a variant of the Lanczos method, inspired by CI, that has the novelty of using as the seed of the Lanczos process a mean field (Hartree–Fock) determinant (the method will be named LCI). Two questions of interest related to model Hamiltonians will be discussed: (i) when including long-range interactions, how crucial is including in the Hamiltonian the electronic charge that compensates ion charges? (ii) Is it possible to reduce a Hamiltonian incorporating Coulomb interactions (PPP) to an ‘effective’ Hamiltonian including only on-site interactions (Hubbard)? The

The role of operator ordering in quantum field theory

International Nuclear Information System (INIS)

Suzuki, Tsuneo; Hirshfeld, A.C.; Leschke, H.

1980-01-01

We study the role of operator ordering in quantum field theory. Operator ordering techniques discussed in our previous papers in the quantum mechanical context are extended to field theory. In this case formally infinite terms appear which must be given a meaning in the framework of some definite regularization scheme. Different orderings for the non-commuting operators in the interaction Hamiltonian lead in general to different expressions for the Dyson-Wick expansion of the S-matrix, implying different Feynman rules. Different orderings correspond to different assignments for the initially undetermined values of the contractions occurring in closed-loop diagrams. Combining a special class of ordering schemes (u-ordering, a generalization of Weyl-ordering) with dimensional regularization leads to important simplifications, and in this case manipulations in which ordering complications are neglected may be justified. We use our methods to discuss gauge invariance in scalar electrodynamics, and the equivalent theorem for a reducible field theoretical model. (author)

Optimal control of open quantum systems: a combined surrogate hamiltonian optimal control theory approach applied to photochemistry on surfaces.

Science.gov (United States)

Asplund, Erik; Klüner, Thorsten

2012-03-28

In this paper, control of open quantum systems with emphasis on the control of surface photochemical reactions is presented. A quantum system in a condensed phase undergoes strong dissipative processes. From a theoretical viewpoint, it is important to model such processes in a rigorous way. In this work, the description of open quantum systems is realized within the surrogate hamiltonian approach [R. Baer and R. Kosloff, J. Chem. Phys. 106, 8862 (1997)]. An efficient and accurate method to find control fields is optimal control theory (OCT) [W. Zhu, J. Botina, and H. Rabitz, J. Chem. Phys. 108, 1953 (1998); Y. Ohtsuki, G. Turinici, and H. Rabitz, J. Chem. Phys. 120, 5509 (2004)]. To gain control of open quantum systems, the surrogate hamiltonian approach and OCT, with time-dependent targets, are combined. Three open quantum systems are investigated by the combined method, a harmonic oscillator immersed in an ohmic bath, CO adsorbed on a platinum surface, and NO adsorbed on a nickel oxide surface. Throughout this paper, atomic units, i.e., ℏ = m(e) = e = a(0) = 1, have been used unless otherwise stated.

Green-Schwarz superstring theory in two dimensions and topological field theories

International Nuclear Information System (INIS)

Igarashi, Yuji; Kubo, Jisuke

1991-01-01

It is shown that the algebra associated with the local Κ-supersymmetry in the Green-Schwarz superstring theory in d=2 dimensions closes of shell. We quantize the theory in a Lorentz covariant fashion by using the generalized hamiltonian method of Batalin, Fradkin and Vilkovisky and derive a quantum mechanically consistent, gauge-fixed theory, which can be interpreted as a Κ-supersymmetric extension of conformal topological gravity. (orig.)

QCD Reggeon field theory for every day: Pomeron loops included

International Nuclear Information System (INIS)

Altinoluk, Tolga; Kovner, Alex; Peressutti, Javier; Lublinsky, Michael

2009-01-01

We derive the evolution equation for hadronic scattering amplitude at high energy. Our derivation includes the nonlinear effects of finite partonic density in the hadronic wave function as well as the effect of multiple scatterings for scattering on dense hadronic target. It thus includes Pomeron loops. It is based on the evolution of the hadronic wave function derived in /cite{foam}. The kernel of the evolution equation defines the second quantized Hamiltonian of the QCD Reggeon Field Theory, H RFT beyond the limits considered so far. The two previously known limits of the evolution: dilute target (JIMWLK limit) and dilute projectile (KLWMIJ limit) are recovered directly from our final result. The Hamiltonian H RFT is applicable for the evolution of scattering amplitude for arbitrarily dense hadronic projectiles/targets - from 'dipole-dipole' to 'nucleus-nucleus' scattering processes.

Deconfinement phase transition in the Hamiltonian approach to Yang–Mills theory in Coulomb gauge

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Reinhardt H.

2014-04-01

Full Text Available Recent results obtained for the deconfinement phase transition within the Hamiltonian approach to Yang–Mills theory are reviewed. Assuming a quasiparticle picture for the grand canonical gluon ensemble the thermal equilibrium state is found by minimizing the free energy with respect to the quasi-gluon energy. The deconfinement phase transition is accompanied by a drastic change of the infrared exponents of the ghost and gluon propagators. Above the phase transition the ghost form factor remains infrared divergent but its infrared exponent is approximately halved. The gluon energy being infrared divergent in the confined phase becomes infrared finite in the deconfined phase. Furthermore, the effective potential of the order parameter for confinement is calculated for SU(N Yang–Mills theory in the Hamiltonian approach by compactifying one spatial dimension and using a background gauge fixing. In the simplest truncation, neglecting the ghost and using the ultraviolet form of the gluon energy, we recover the Weiss potential. From the full non-perturbative potential (with the ghost included we extract a critical temperature of the deconfinement phase transition of 269 MeV for the gauge group SU(2 and 283 MeV for SU(3.

Effective field theory of thermal Casimir interactions between anisotropic particles.

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Haussman, Robert C; Deserno, Markus

2014-06-01

We employ an effective field theory (EFT) approach to study thermal Casimir interactions between objects bound to a fluctuating fluid surface or interface dominated by surface tension, with a focus on the effects of particle anisotropy. The EFT prescription disentangles the constraints imposed by the particles' boundaries from the calculation of the interaction free energy by constructing an equivalent point particle description. The finite-size information is captured in a derivative expansion that encodes the particles' response to external fields. The coefficients of the expansion terms correspond to generalized tensorial polarizabilities and are found by matching the results of a linear response boundary value problem computed in both the full and effective theories. We demonstrate the versatility of the EFT approach by constructing the general effective Hamiltonian for a collection of particles of arbitrary shapes. Taking advantage of the conformal symmetry of the Hamiltonian, we discuss a straightforward conformal mapping procedure to systematically determine the polarizabilities and derive a complete description for elliptical particles. We compute the pairwise interaction energies to several orders for nonidentical ellipses as well as their leading-order triplet interactions and discuss the resulting preferred pair and multibody configurations. Furthermore, we elaborate on the complications that arise with pinned particle boundary conditions and show that the powerlike corrections expected from dimensional analysis are exponentially suppressed by the leading-order interaction energies.

Chiral Schwinger model with the Faddeevian regularization in the light-front frame: construction of the gauge-invariant theory through the Stueckelberg term, Hamiltonian and BRST formulations

International Nuclear Information System (INIS)

Kulshreshtha, U.

1998-01-01

A chiral Schwinger model with the Faddeevian regularization a la Mitra is studied in the light-front frame. The front-form theory is found to be gauge-non-invariant. The Hamiltonian formulation of this gauge-non-invariant theory is first investigated and then the Stueckelberg term for this theory is constructed. Finally, the Hamiltonian and BRST formulations of the resulting gauge-invariant theory, obtained by the inclusion of the Stueckelberg term in the action of the above gauge-non-invariant theory, are investigated with some specific gauge choices. (orig.)

Boundary Hamiltonian Theory for Gapped Topological Orders

Science.gov (United States)

Hu, Yuting; Wan, Yidun; Wu, Yong-Shi

2017-06-01

We report our systematic construction of the lattice Hamiltonian model of topological orders on open surfaces, with explicit boundary terms. We do this mainly for the Levin-Wen string-net model. The full Hamiltonian in our approach yields a topologically protected, gapped energy spectrum, with the corresponding wave functions robust under topology-preserving transformations of the lattice of the system. We explicitly present the wavefunctions of the ground states and boundary elementary excitations. The creation and hopping operators of boundary quasi-particles are constructed. It is found that given a bulk topological order, the gapped boundary conditions are classified by Frobenius algebras in its input data. Emergent topological properties of the ground states and boundary excitations are characterized by (bi-) modules over Frobenius algebras.

Discrete variational Hamiltonian mechanics

International Nuclear Information System (INIS)

Lall, S; West, M

2006-01-01

The main contribution of this paper is to present a canonical choice of a Hamiltonian theory corresponding to the theory of discrete Lagrangian mechanics. We make use of Lagrange duality and follow a path parallel to that used for construction of the Pontryagin principle in optimal control theory. We use duality results regarding sensitivity and separability to show the relationship between generating functions and symplectic integrators. We also discuss connections to optimal control theory and numerical algorithms

Extension of the CPT theorem to non-Hermitian Hamiltonians and unstable states

Energy Technology Data Exchange (ETDEWEB)

Mannheim, Philip D., E-mail: philip.mannheim@uconn.edu

2016-02-10

We extend the CPT theorem to quantum field theories with non-Hermitian Hamiltonians and unstable states. Our derivation is a quite minimal one as it requires only the time-independent evolution of scalar products, invariance under complex Lorentz transformations, and a non-standard but nonetheless perfectly legitimate interpretation of charge conjugation as an antilinear operator. The first of these requirements does not force the Hamiltonian to be Hermitian. Rather, it forces its eigenvalues to either be real or to appear in complex conjugate pairs, forces the eigenvectors of such conjugate pairs to be conjugates of each other, and forces the Hamiltonian to admit of an antilinear symmetry. The latter two requirements then force this antilinear symmetry to be CPT, while forcing the Hamiltonian to be real rather than Hermitian. Our work justifies the use of the CPT theorem in establishing the equality of the lifetimes of unstable particles that are charge conjugates of each other. We show that the Euclidean time path integrals of a CPT-symmetric theory must always be real. In the quantum-mechanical limit the key results of the PT symmetry program of Bender and collaborators are recovered, with the C-operator of the PT symmetry program being identified with the linear component of the charge conjugation operator.

Modular Hamiltonians for deformed half-spaces and the averaged null energy condition

Science.gov (United States)

Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar; Wang, Huajia

2016-09-01

We study modular Hamiltonians corresponding to the vacuum state for deformed half-spaces in relativistic quantum field theories on {{R}}^{1,d-1} . We show that in addition to the usual boost generator, there is a contribution to the modular Hamiltonian at first order in the shape deformation, proportional to the integral of the null components of the stress tensor along the Rindler horizon. We use this fact along with monotonicity of relative entropy to prove the averaged null energy condition in Minkowski space-time. This subsequently gives a new proof of the Hofman-Maldacena bounds on the parameters appearing in CFT three-point functions. Our main technical advance involves adapting newly developed perturbative methods for calculating entanglement entropy to the problem at hand. These methods were recently used to prove certain results on the shape dependence of entanglement in CFTs and here we generalize these results to excited states and real time dynamics. We also discuss the AdS/CFT counterpart of this result, making connection with the recently proposed gravitational dual for modular Hamiltonians in holographic theories.

Effective Floquet Hamiltonian theory of multiple-quantum NMR in anisotropic solids involving quadrupolar spins: Challenges and Perspectives

Science.gov (United States)

Ganapathy, Vinay; Ramachandran, Ramesh

2017-10-01

The response of a quadrupolar nucleus (nuclear spin with I > 1/2) to an oscillating radio-frequency pulse/field is delicately dependent on the ratio of the quadrupolar coupling constant to the amplitude of the pulse in addition to its duration and oscillating frequency. Consequently, analytic description of the excitation process in the density operator formalism has remained less transparent within existing theoretical frameworks. As an alternative, the utility of the "concept of effective Floquet Hamiltonians" is explored in the present study to explicate the nuances of the excitation process in multilevel systems. Employing spin I = 3/2 as a case study, a unified theoretical framework for describing the excitation of multiple-quantum transitions in static isotropic and anisotropic solids is proposed within the framework of perturbation theory. The challenges resulting from the anisotropic nature of the quadrupolar interactions are addressed within the effective Hamiltonian framework. The possible role of the various interaction frames on the convergence of the perturbation corrections is discussed along with a proposal for a "hybrid method" for describing the excitation process in anisotropic solids. Employing suitable model systems, the validity of the proposed hybrid method is substantiated through a rigorous comparison between simulations emerging from exact numerical and analytic methods.

Testing the master constraint programme for loop quantum gravity: V. Interacting field theories

International Nuclear Information System (INIS)

Dittrich, B; Thiemann, T

2006-01-01

This is the fifth and final paper in our series of five in which we test the master constraint programme for solving the Hamiltonian constraint in loop quantum gravity. Here we consider interacting quantum field theories, specifically we consider the non-Abelian Gauss constraints of Einstein-Yang-Mills theory and 2 + 1 gravity. Interestingly, while Yang-Mills theory in 4D is not yet rigorously defined as an ordinary (Wightman) quantum field theory on Minkowski space, in background-independent quantum field theories such as loop quantum gravity (LQG) this might become possible by working in a new, background-independent representation. While for the Gauss constraint the master constraint can be solved explicitly, for the 2 + 1 theory we are only able to rigorously define the master constraint operator. We show that the, by other methods known, physical Hilbert is contained in the kernel of the master constraint, however, to systematically derive it by only using spectral methods is as complicated as for 3 + 1 gravity and we therefore leave the complete analysis for 3 + 1 gravity

Canonical transformation path to gauge theories of gravity

Science.gov (United States)

Struckmeier, J.; Muench, J.; Vasak, D.; Kirsch, J.; Hanauske, M.; Stoecker, H.

2017-06-01

In this paper, the generic part of the gauge theory of gravity is derived, based merely on the action principle and on the general principle of relativity. We apply the canonical transformation framework to formulate geometrodynamics as a gauge theory. The starting point of our paper is constituted by the general De Donder-Weyl Hamiltonian of a system of scalar and vector fields, which is supposed to be form-invariant under (global) Lorentz transformations. Following the reasoning of gauge theories, the corresponding locally form-invariant system is worked out by means of canonical transformations. The canonical transformation approach ensures by construction that the form of the action functional is maintained. We thus encounter amended Hamiltonian systems which are form-invariant under arbitrary spacetime transformations. This amended system complies with the general principle of relativity and describes both, the dynamics of the given physical system's fields and their coupling to those quantities which describe the dynamics of the spacetime geometry. In this way, it is unambiguously determined how spin-0 and spin-1 fields couple to the dynamics of spacetime. A term that describes the dynamics of the "free" gauge fields must finally be added to the amended Hamiltonian, as common to all gauge theories, to allow for a dynamic spacetime geometry. The choice of this "dynamics" Hamiltonian is outside of the scope of gauge theory as presented in this paper. It accounts for the remaining indefiniteness of any gauge theory of gravity and must be chosen "by hand" on the basis of physical reasoning. The final Hamiltonian of the gauge theory of gravity is shown to be at least quadratic in the conjugate momenta of the gauge fields—this is beyond the Einstein-Hilbert theory of general relativity.

Incomplete Dirac reduction of constrained Hamiltonian systems

Energy Technology Data Exchange (ETDEWEB)

Chandre, C., E-mail: chandre@cpt.univ-mrs.fr

2015-10-15

First-class constraints constitute a potential obstacle to the computation of a Poisson bracket in Dirac’s theory of constrained Hamiltonian systems. Using the pseudoinverse instead of the inverse of the matrix defined by the Poisson brackets between the constraints, we show that a Dirac–Poisson bracket can be constructed, even if it corresponds to an incomplete reduction of the original Hamiltonian system. The uniqueness of Dirac brackets is discussed. The relevance of this procedure for infinite dimensional Hamiltonian systems is exemplified.

An introduction to some mathematical aspects of scattering theory in models of quantum fields

International Nuclear Information System (INIS)

Albeverio, S.

1974-01-01

An elementary introduction is given to some results, problems and methods of the recent study of scattering in models developed in connection with constructive quantum field theory. A deliberate effort has been made to be understandable also for mathematicians having some notions of non-relativistic quantum mechanics but no specific previous knowledge of quantum field theory. The Fock space, the free fields and the free Hamiltonian are introduced and the singular perturbation problem posed by local relativistic interaction is discussed. Scattering theory is first discussed for the simplified cases of space cut-off interactions and of translation invariant interactions with persistent vacuum. The Wightman-Haag-Ruelle axiomatic framework is given as a guide for the construction of models with local, relativistic interactions and of the corresponding scattering theory. The verification of the axioms is carried through in a class of models with local relativistic interactions in two-dimensional space-time. (Auth.)

Noncanonical Hamiltonian mechanics

International Nuclear Information System (INIS)

Litteljohn, R.G.

1986-01-01

Noncanonical variables in Hamiltonian mechanics were first used by Lagrange in 1808. In spite of this, most work in Hamiltonian mechanics has been carried out in canonical variables, up to this day. One reason for this is that noncanonical coordinates are seldom needed for mechanical problems based on Lagrangians of the form L = T - V, where T is the kinetic energy and V is the potential energy. Of course, such Lagrangians arise naturally in celestial mechanics, and as a result they form the paradigms of nineteenth-century mechanics and have become enshrined in all the mechanics textbooks. Certain features of modern problems, however, lead to the use of noncanonical coordinates. Among these are issues of gauge invariance and singular Lagrange a Poisson structures. In addition, certain problems, like the flow of magnetic-field lines in physical space, are naturally formulated in terms of noncanonical coordinates. None of these features is present in the nineteenth-century paradigms of mechanics, but they do arise in problems involving particle motion in the presence of magnetic fields. For example, the motion of a particle in an electromagnetic wave is an important one in plasma physics, but the usual Hamiltonian formulation is gauge dependent. For this problem, noncanonical approaches based on Lagrangians in phase space lead to powerful computational techniques which are gauge invariant. In the limit of strong magnetic fields, particle motion becomes 'guiding-center motion'. Guiding-center motion is also best understood in terms of noncanonical coordinates. Finally the flow of magnetic-field lines through physical space is a Hamiltonian system which is best understood with noncanonical coordinates. No doubt many more systems will arise in the future for which these noncanonical techniques can be applied. (author)

Existence for stationary mean-field games with congestion and quadratic Hamiltonians

KAUST Repository

Gomes, Diogo A.

2015-09-03

Here, we investigate the existence of solutions to a stationary mean-field game model introduced by J.-M. Lasry and P.-L. Lions. This model features a quadratic Hamiltonian and congestion effects. The fundamental difficulty of potential singular behavior is caused by congestion. Thanks to a new class of a priori bounds, combined with the continuation method, we prove the existence of smooth solutions in arbitrary dimensions. © 2015 Springer Basel

Hamiltonian analysis of transverse dynamics in axisymmetric rf photoinjectors

International Nuclear Information System (INIS)

Wang, C.-x.

2006-01-01

A general Hamiltonian that governs the beam dynamics in an rf photoinjector is derived from first principles. With proper choice of coordinates, the resulting Hamiltonian has a simple and familiar form, while taking into account the rapid acceleration, rf focusing, magnetic focusing, and space-charge forces. From the linear Hamiltonian, beam-envelope evolution is readily obtained, which better illuminates the theory of emittance compensation. Preliminary results on the third-order nonlinear Hamiltonian will be given as well.

Dissipation Effects in Schrödinger and Quantal Density Functional Theories of Electrons in an Electromagnetic Field

Directory of Open Access Journals (Sweden)

Xiao-Yin Pan

2018-03-01

Full Text Available Dissipative effects arise in an electronic system when it interacts with a time-dependent environment. Here, the Schrödinger theory of electrons in an electromagnetic field including dissipative effects is described from a new perspective. Dissipation is accounted for via the effective Hamiltonian approach in which the electron mass is time-dependent. The perspective is that of the individual electron: the corresponding equation of motion for the electron or time-dependent differential virial theorem—the ‘Quantal Newtonian’ second law—is derived. According to the law, each electron experiences an external field comprised of a binding electric field, the Lorentz field, and the electromagnetic field. In addition, there is an internal field whose components are representative of electron correlations due to the Pauli exclusion principle and Coulomb repulsion, kinetic effects, and density. There is also an internal contribution due to the magnetic field. The response of the electron is governed by the current density field in which a damping coefficient appears. The law leads to further insights into Schrödinger theory, and in particular the intrinsic self-consistent nature of the Schrödinger equation. It is proved that in the presence of dissipative effects, the basic variables (gauge-invariant properties, knowledge of which determines the Hamiltonian are the density and physical current density. Finally, a local effective potential theory of dissipative systems—quantal density functional theory (QDFT—is developed. This constitutes the mapping from the interacting dissipative electronic system to one of noninteracting fermions possessing the same dissipation and basic variables. Attributes of QDFT are the separation of the electron correlations due to the Pauli exclusion principle and Coulomb repulsion, and the determination of the correlation contributions to the kinetic energy. Hence, Schrödinger theory in conjunction with QDFT

Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory

Science.gov (United States)

Rohringer, G.; Hafermann, H.; Toschi, A.; Katanin, A. A.; Antipov, A. E.; Katsnelson, M. I.; Lichtenstein, A. I.; Rubtsov, A. N.; Held, K.

2018-04-01

Strong electronic correlations pose one of the biggest challenges to solid state theory. Recently developed methods that address this problem by starting with the local, eminently important correlations of dynamical mean field theory (DMFT) are reviewed. In addition, nonlocal correlations on all length scales are generated through Feynman diagrams, with a local two-particle vertex instead of the bare Coulomb interaction as a building block. With these diagrammatic extensions of DMFT long-range charge, magnetic, and superconducting fluctuations as well as (quantum) criticality can be addressed in strongly correlated electron systems. An overview is provided of the successes and results achieved, mainly for model Hamiltonians, and an outline is given of future prospects for realistic material calculations.

Integrable and nonintegrable non-KAM Hamiltonians and magnetic field topology

International Nuclear Information System (INIS)

Salat, A.

1986-01-01

The integrability of Hamiltonians H(P 1 , P 2 , Q 1 , Q 2 )=P 1 G 1 (Q 1 ,Q 2 )+P 2 G 2 (Q 1 ,Q 2 ), with arbitrary analytic G 1 and G 2 , 2π-periodic in Q 1 and Q 2 , is analytically investigated. Such H cannot be separated into two parts, H=H 0 +H 21 , such that the KAM theorem would apply for vertical strokeH 1 vertical stroke 0 vertical stroke. For G 2 =const such Hamiltonians correspond to toroidal magnetic fields with constant rotational transform. Integrability is then equivalent to the existence of closed magnetic surfaces. The winding number w of the Q 1 , Q 2 flow (i.e. the rotational transform) is rational in 'tongue'-like domains in (ω 2 /ω 1 ,A) diagrams. Here ω i = i > is the average over both Q 1 and Q 2 , G i =ω i +F i , i=1, 2, and A is an amplitude parameter of F i (F i =0 for A=0). Integrability is proved almost everywhere in the complementary domains, namely where w is sufficiently irrational. In the generic case ('conditional') nonintegrability is proved for the class dG 1 /dQ 1 +dG 2 /dQ 2 =0 in the tongues, which in this case shrink to lines with w=ω 1 /ω 2 . It is shown that if the number of dimensions in the Hamiltonian were larger than two, qualitatively different results would be expected. (orig.)

A diagrammatic construction of formal E-independent model hamiltonian

International Nuclear Information System (INIS)

Kvasnicka, V.

1977-01-01

A diagrammatic construction of formal E-independent model interaction (i.e., without second-quantization formalism) is suggested. The construction starts from the quasi-degenerate Brillouin-Wigner perturbation theory, in the framework of which an E-dependent model Hamiltonian is simply constructed. Applying the ''E-removing'' procedure to this E-dependent model Hamiltonian, the E-independent formal model Hamiltonian either Hermitian or non-Hermitian can diagrammatically be easily derived. For the formal E-independent model Hamiltonian the separability theorem is proved, which can be profitably used for a rather ''formalistic ''construction of a many-body E-independent model Hamiltonian

Hamiltonian field description of the one-dimensional Poisson-Vlasov equations

International Nuclear Information System (INIS)

Morrison, P.J.

1981-07-01

The one-dimensional Poisson-Vlasov equations are cast into Hamiltonian form. A Poisson Bracket in terms of the phase space density, as sole dynamical variable, is presented. This Poisson bracket is not of the usual form, but possesses the commutator properties of antisymmetry, bilinearity, and nonassociativity by virtue of the Jacobi requirement. Clebsch potentials are seen to yield a conventional (canonical) formulation. This formulation is discretized by expansion in terms of an arbitrary complete set of basis functions. In particular, a wave field representation is obtained

Optimal control of open quantum systems: A combined surrogate Hamiltonian optimal control theory approach applied to photochemistry on surfaces

International Nuclear Information System (INIS)

Asplund, Erik; Kluener, Thorsten

2012-01-01

In this paper, control of open quantum systems with emphasis on the control of surface photochemical reactions is presented. A quantum system in a condensed phase undergoes strong dissipative processes. From a theoretical viewpoint, it is important to model such processes in a rigorous way. In this work, the description of open quantum systems is realized within the surrogate Hamiltonian approach [R. Baer and R. Kosloff, J. Chem. Phys. 106, 8862 (1997)]. An efficient and accurate method to find control fields is optimal control theory (OCT) [W. Zhu, J. Botina, and H. Rabitz, J. Chem. Phys. 108, 1953 (1998); Y. Ohtsuki, G. Turinici, and H. Rabitz, J. Chem. Phys. 120, 5509 (2004)]. To gain control of open quantum systems, the surrogate Hamiltonian approach and OCT, with time-dependent targets, are combined. Three open quantum systems are investigated by the combined method, a harmonic oscillator immersed in an ohmic bath, CO adsorbed on a platinum surface, and NO adsorbed on a nickel oxide surface. Throughout this paper, atomic units, i.e., (ℎ/2π)=m e =e=a 0 = 1, have been used unless otherwise stated.

Quantum finance Hamiltonian for coupon bond European and barrier options.

Science.gov (United States)

Baaquie, Belal E

2008-03-01

Coupon bond European and barrier options are financial derivatives that can be analyzed in the Hamiltonian formulation of quantum finance. Forward interest rates are modeled as a two-dimensional quantum field theory and its Hamiltonian and state space is defined. European and barrier options are realized as transition amplitudes of the time integrated Hamiltonian operator. The double barrier option for a financial instrument is "knocked out" (terminated with zero value) if the price of the underlying instrument exceeds or falls below preset limits; the barrier option is realized by imposing boundary conditions on the eigenfunctions of the forward interest rates' Hamiltonian. The price of the European coupon bond option and the zero coupon bond barrier option are calculated. It is shown that, is general, the constraint function for a coupon bond barrier option can -- to a good approximation -- be linearized. A calculation using an overcomplete set of eigenfunctions yields an approximate price for the coupon bond barrier option, which is given in the form of an integral of a factor that results from the barrier condition times another factor that arises from the payoff function.

The investigation of 1+1 dimensional lattice gauge theories with fermions, gauge bosons and scalar using Hamiltonian Monte-Carlo methods

International Nuclear Information System (INIS)

Ranft, J.

1984-01-01

Hamiltonian lattice models with fermions, gauge bosons and scalar fields are studied in 1+1 dimensions using the local Hamiltonian Monte-Carlo method. Results are presented for the massive Schwinger model with one and two flavors, for a model with interacting Higgs fields, fermions and gauge bosons, where fractionally charged solitons are found as free states of the lattice model, and for Wess-Zumino type models with restricted lattice supersymmetry, where examples for spontaneous breaking of supersymmetry are found

15th International Conference on Non-Hermitian Hamiltonians in Quantum Physics

CERN Document Server

Passante, Roberto; Trapani, Camillo

2016-01-01

This book presents the Proceedings of the 15th International Conference on Non-Hermitian Hamiltonians in Quantum Physics, held in Palermo, Italy, from 18 to 23 May 2015. Non-Hermitian operators, and non-Hermitian Hamiltonians in particular, have recently received considerable attention from both the mathematics and physics communities. There has been a growing interest in non-Hermitian Hamiltonians in quantum physics since the discovery that PT-symmetric Hamiltonians can have a real spectrum and thus a physical relevance. The main subjects considered in this book include: PT-symmetry in quantum physics, PT-optics, Spectral singularities and spectral techniques, Indefinite-metric theories, Open quantum systems, Krein space methods, and Biorthogonal systems and applications. The book also provides a summary of recent advances in pseudo-Hermitian Hamiltonians and PT-symmetric Hamiltonians, as well as their applications in quantum physics and in the theory of open quantum systems.

A general theory for gauge-free lifting

International Nuclear Information System (INIS)

Morrison, P. J.

2013-01-01

A theory for lifting equations of motion for charged particle dynamics, subject to given electromagnetic like forces, up to a gauge-free system of coupled Hamiltonian Vlasov-Maxwell like equations is given. The theory provides very general expressions for the polarization and magnetization vector fields in terms of the particle dynamics description of matter. Thus, as is common in plasma physics, the particle dynamics replaces conventional constitutive relations for matter. Several examples are considered including the usual Vlasov-Maxwell theory, a guiding center kinetic theory, Vlasov-Maxwell theory with the inclusion of spin, and a Vlasov-Maxwell theory with the inclusion of Dirac's magnetic monopoles. All are shown to be Hamiltonian field theories and the Jacobi identity is proven directly.

Variational identities and Hamiltonian structures

International Nuclear Information System (INIS)

Ma Wenxiu

2010-01-01

This report is concerned with Hamiltonian structures of classical and super soliton hierarchies. In the classical case, basic tools are variational identities associated with continuous and discrete matrix spectral problems, targeted to soliton equations derived from zero curvature equations over general Lie algebras, both semisimple and non-semisimple. In the super case, a supertrace identity is presented for constructing Hamiltonian structures of super soliton equations associated with Lie superalgebras. We illustrate the general theories by the KdV hierarchy, the Volterra lattice hierarchy, the super AKNS hierarchy, and two hierarchies of dark KdV equations and dark Volterra lattices. The resulting Hamiltonian structures show the commutativity of each hierarchy discussed and thus the existence of infinitely many commuting symmetries and conservation laws.

Linked-cluster perturbation theory for closed and open-shell systems: derivation of effective π-electron hamiltonians

International Nuclear Information System (INIS)

Brandow, B.H.

1977-01-01

The Brueckner--Goldstone form of linked-cluster perturbation theory is derived, together with its open-shell analog, by an elementary time-independent approach. This serves to focus attention on the physical interpretation of the results. The open-shell expansion is used to provide a straightforward justification for the effective π-electron Hamiltonians of planar organic molecules

Hamiltonian formalisms and symmetries of the Pais–Uhlenbeck oscillator

Directory of Open Access Journals (Sweden)

Krzysztof Andrzejewski

2014-12-01

Full Text Available The study of the symmetry of Pais–Uhlenbeck oscillator initiated in Andrzejewski et al. (2014 [24] is continued with special emphasis put on the Hamiltonian formalism. The symmetry generators within the original Pais and Uhlenbeck Hamiltonian approach as well as the canonical transformation to the Ostrogradski Hamiltonian framework are derived. The resulting algebra of generators appears to be the central extension of the one obtained on the Lagrangian level; in particular, in the case of odd frequencies one obtains the centrally extended l-conformal Newton–Hooke algebra. In this important case the canonical transformation to an alternative Hamiltonian formalism (related to the free higher derivatives theory is constructed. It is shown that all generators can be expressed in terms of the ones for the free theory and the result agrees with that obtained by the orbit method.

Terminological confusions and problems at the interface between the crystal field Hamiltonians and the zero-field splitting Hamiltonians—Survey of the CF=ZFS confusion in recent literature

Energy Technology Data Exchange (ETDEWEB)

Rudowicz, Czesław, E-mail: crudowicz@zut.edu.pl [Institute of Physics, West Pomeranian University of Technology, Al. Piastów 17, 70-310 Szczecin (Poland); Karbowiak, Mirosław [Faculty of Chemistry, University of Wrocław, ul. F. Joliot-Curie 14, 50-383 Wrocław (Poland)

2014-10-15

The single transition ions in various crystals or molecules as well as the exchange coupled systems (ECS) of transition ions, especially the single molecule magnets (SMM) or molecular nanomagnets (MNM), have been extensively studied in recent decades using electron magnetic resonance (EMR), optical spectroscopy, and magnetic measurements. Interpretation of magnetic and spectroscopic properties of transition ions is based on two physically distinct types of Hamiltonians: the physical crystal field (CF), or equivalently ligand field (LF), Hamiltonians and the effective spin Hamiltonians (SH), which include the zero-field splitting (ZFS) Hamiltonians. Survey of recent literature has revealed a number of terminological confusions and specific problems occurring at the interface between these Hamiltonians (denoted CF (LF)↔SH (ZFS)). Elucidation of sloppy or incorrect usage of crucial notions, especially those describing or parameterizing crystal fields and zero field splittings, is a very challenging task that requires several reviews. Here we focus on the prevailing confusion between the CF (LF) and SH (ZFS) quantities, denoted as the CF=ZFS confusion, which consists in referring to the parameters (or Hamiltonians), which are the true ZFS (or SH) quantities, as purportedly the CF (LF) quantities. The inverse ZFS=CF confusion, which pertains to the cases of labeling the true CF (LF) quantities as purportedly the ZFS quantities, is considered in a follow-up paper. The two reviews prepare grounds for a systematization of nomenclature aimed at bringing order to the zoo of different Hamiltonians. Specific cases of the CF=ZFS confusion identified in the recent textbooks, review articles, and SMM (MNM)- and EMR-related papers are surveyed and the pertinent misconceptions are outlined. The consequences of the terminological confusions go far beyond simple semantic issues or misleading keyword classifications of papers in journals and scientific databases. Serious

Resolving the issue of branched Hamiltonian in modified Lanczos-Lovelock gravity

Science.gov (United States)

Ruz, Soumendranath; Mandal, Ranajit; Debnath, Subhra; Sanyal, Abhik Kumar

2016-07-01

The Hamiltonian constraint H_c = N{H} = 0, defines a diffeomorphic structure on spatial manifolds by the lapse function N in general theory of relativity. However, it is not manifest in Lanczos-Lovelock gravity, since the expression for velocity in terms of the momentum is multivalued. Thus the Hamiltonian is a branch function of momentum. Here we propose an extended theory of Lanczos-Lovelock gravity to construct a unique Hamiltonian in its minisuperspace version, which results in manifest diffeomorphic invariance and canonical quantization.

Hamiltonian theory of the ion cyclotron minority heating dynamics in tokamak plasmas

International Nuclear Information System (INIS)

Becoulet, A.; Gambier, D.J.; Samain, A.

1990-03-01

The question of heating a tokamak plasma by means of electromagnetic waves in the Ion Cyclotron Range of Frequency (ICRF) is considered in the perspective of large RF powers and in the low collisionality regime. In such case the Quasi Linear Theory (QLT) is validated by the Hamiltonian dynamics of the wave particle interaction which exceeds the threshold of the intrinsic stochasticity. The Hamiltonian dynamics is represented by the evolution of a set of three canonical action angle variables well adapted to the tokamak magnetic configuration. This approach allows to derive the RF diffusion coefficient with very few assumptions. The distribution function of the resonant ions is written as a Fokker Planck equation but the emphasis is put on the QL diffusion instead of on the usual diffusion induced by collisions. Then the Fokker Planck equation is given a variational from which a solution is derived in the form of a semi analytical trial function of three parameters: the percentage of resonant particle contained in the tail; an isotropic width ΔT and an anisotropic one ΔP. This solution is successfully tested against real experimental observations. Practically it is shown that in the case of JET the distribution function is influenced by adiabatic barriers which in turn limit the Hamiltonian stochasticity domain within energy values typically in the MeV range. Consequently and for a given ICRF power, the tail energy excursion is lower and its concentration higher than that of a bounce averaged prediction. This may actually be an advantage for machines like JET considering the energy range required to simulate the α-particle behaviour in a relevant fusion reactor

Exact smooth classification of Hamiltonian vector fields on symplectic 2-manifolds

International Nuclear Information System (INIS)

Krouglikov, B.S.

1994-10-01

Complete exact classification of Hamiltonian systems with one degree of freedom and Morse Hamiltonian is carried out. As it is a main part of trajectory classification of integrable Hamiltonian systems with two degrees of freedom, the corresponding generalization is considered. The dual problem of classification of symplectic form together with Morse foliation is carried out as well. (author). 10 refs, 16 figs

Spinning gravitating objects in the effective field theory in the post-Newtonian scheme

Energy Technology Data Exchange (ETDEWEB)

Levi, Michele [Université Pierre et Marie Curie-Paris VI, CNRS-UMR 7095,Institut d’Astrophysique de Paris, 98 bis Boulevard Arago, 75014 Paris (France); Sorbonne Universités, Institut Lagrange de Paris,98 bis Boulevard Arago, 75014 Paris (France); Steinhoff, Jan [Max-Planck-Institute for Gravitational Physics (Albert-Einstein-Institute),Am Mühlenberg 1, 14476 Potsdam-Golm (Germany); Centro Multidisciplinar de Astrofisica, Instituto Superior Tecnico, Universidade de Lisboa,Avenida Rovisco Pais 1, 1049-001 Lisboa (Portugal)

2015-09-30

We introduce a formulation for spinning gravitating objects in the effective field theory in the post-Newtonian scheme in the context of the binary inspiral problem. We aim at an effective action, where all field modes below the orbital scale are integrated out. We spell out the relevant degrees of freedom, in particular the rotational ones, and the associated symmetries. Building on these symmetries, we introduce the minimal coupling part of the point particle action in terms of gauge rotational variables, and construct the spin-induced nonminimal couplings, where we obtain the leading order couplings to all orders in spin. We specify the gauge for the rotational variables, where the unphysical degrees of freedom are eliminated already from the Feynman rules, and all the orbital field modes are integrated out. The equations of motion of the spin can be directly obtained via a proper variation of the action, and Hamiltonians may be straightforwardly derived. We implement this effective field theory for spin to derive all spin dependent potentials up to next-to-leading order to quadratic level in spin, namely up to the third post-Newtonian order for rapidly rotating compact objects. In particular, the proper next-to-leading order spin-squared potential and Hamiltonian for generic compact objects are also derived. For the implementations we use the nonrelativistic gravitational field decomposition, which is found here to eliminate higher-loop Feynman diagrams also in spin dependent sectors, and facilitates derivations. This formulation for spin is thus ideal for treatment of higher order spin dependent sectors.

New Hamiltonians for loop quantum cosmology with arbitrary spin representations

Science.gov (United States)

Ben Achour, Jibril; Brahma, Suddhasattwa; Geiller, Marc

2017-04-01

In loop quantum cosmology, one has to make a choice of SU(2) irreducible representation in which to compute holonomies and regularize the curvature of the connection. The systematic choice made in the literature is to work in the fundamental representation, and very little is known about the physics associated with higher spin labels. This constitutes an ambiguity of which the understanding, we believe, is fundamental for connecting loop quantum cosmology to full theories of quantum gravity like loop quantum gravity, its spin foam formulation, or cosmological group field theory. We take a step in this direction by providing here a new closed formula for the Hamiltonian of flat Friedmann-Lemaître-Robertson-Walker models regularized in a representation of arbitrary spin. This expression is furthermore polynomial in the basic variables which correspond to well-defined operators in the quantum theory, takes into account the so-called inverse-volume corrections, and treats in a unified way two different regularization schemes for the curvature. After studying the effective classical dynamics corresponding to single and multiple-spin Hamiltonians, we study the behavior of the critical density when the number of representations is increased and the stability of the difference equations in the quantum theory.

Topological color codes and two-body quantum lattice Hamiltonians

Science.gov (United States)

Kargarian, M.; Bombin, H.; Martin-Delgado, M. A.

2010-02-01

Topological color codes are among the stabilizer codes with remarkable properties from the quantum information perspective. In this paper, we construct a lattice, the so-called ruby lattice, with coordination number 4 governed by a two-body Hamiltonian. In a particular regime of coupling constants, in a strong coupling limit, degenerate perturbation theory implies that the low-energy spectrum of the model can be described by a many-body effective Hamiltonian, which encodes the color code as its ground state subspace. Ground state subspace corresponds to a vortex-free sector. The gauge symmetry Z2×Z2 of the color code could already be realized by identifying three distinct plaquette operators on the ruby lattice. All plaquette operators commute with each other and with the Hamiltonian being integrals of motion. Plaquettes are extended to closed strings or string-net structures. Non-contractible closed strings winding the space commute with Hamiltonian but not always with each other. This gives rise to exact topological degeneracy of the model. A connection to 2-colexes can be established via the coloring of the strings. We discuss it at the non-perturbative level. The particular structure of the two-body Hamiltonian provides a fruitful interpretation in terms of mapping onto bosons coupled to effective spins. We show that high-energy excitations of the model have fermionic statistics. They form three families of high-energy excitations each of one color. Furthermore, we show that they belong to a particular family of topological charges. The emergence of invisible charges is related to the string-net structure of the model. The emerging fermions are coupled to nontrivial gauge fields. We show that for particular 2-colexes, the fermions can see the background fluxes in the ground state. Also, we use the Jordan-Wigner transformation in order to test the integrability of the model via introducing Majorana fermions. The four-valent structure of the lattice prevents the

Dirac-bracket aproach to nearly-geostrophic Hamiltonian balanced models

NARCIS (Netherlands)

Vanneste, J.; Bokhove, Onno

2002-01-01

Dirac’s theory of constrained Hamiltonian systems is applied to derive the Poisson structure of a class of balanced models describing the slow dynamics of geophysical flows. Working with the Poisson structure, instead of the canonical Hamiltonian structure previously considered in this context,

Experimental status of unified theories

International Nuclear Information System (INIS)

Bilen'kij, S.M.

1979-01-01

A standard SU(2)xU(1) theory is discussed. It is based on an assumption that the left components of fields form doublets, and the rignt ones - singlets. From the weak interaction lagrangian an expression is obtained for the effective hamiltonian describing neutrino-lepton processes. The results of discussing the experimental status of the unified theories of weak and electromagnetic interactions are in agreement with the simplest version of the unified theories - the Weinberg-Salam theory. It has been noted that the accuracy of the experiments (not exceeding 20%) is insufficient and no information is available on diagonal terms of the hamiltonian

Investigation of timing effects in modified composite quadrupolar echo pulse sequences by mean of average Hamiltonian theory

Science.gov (United States)

Mananga, Eugene Stephane

2018-01-01

The utility of the average Hamiltonian theory and its antecedent the Magnus expansion is presented. We assessed the concept of convergence of the Magnus expansion in quadrupolar spectroscopy of spin-1 via the square of the magnitude of the average Hamiltonian. We investigated this approach for two specific modified composite pulse sequences: COM-Im and COM-IVm. It is demonstrated that the size of the square of the magnitude of zero order average Hamiltonian obtained on the appropriated basis is a viable approach to study the convergence of the Magnus expansion. The approach turns to be efficient in studying pulse sequences in general and can be very useful to investigate coherent averaging in the development of high resolution NMR technique in solids. This approach allows comparing theoretically the two modified composite pulse sequences COM-Im and COM-IVm. We also compare theoretically the current modified composite sequences (COM-Im and COM-IVm) to the recently published modified composite pulse sequences (MCOM-I, MCOM-IV, MCOM-I_d, MCOM-IV_d).

Astrophysical evidence for the non-Hermitian but PT-symmetric Hamiltonian of conformal gravity

International Nuclear Information System (INIS)

Mannheim, P.D.

2013-01-01

In this review we discuss the connection between two seemingly disparate topics, macroscopic gravity on astrophysical scales and Hamiltonians that are not Hermitian but PT symmetric on microscopic ones. In particular we show that the quantum-mechanical unitarity problem of the fourth-order derivative conformal gravity theory is resolved by recognizing that the scalar product appropriate to the theory is not the Dirac norm associated with a Hermitian Hamiltonian but is instead the norm associated with a non-Hermitian but PT-symmetric Hamiltonian. Moreover, the fourth-order theory Hamiltonian is not only not Hermitian, it is not even diagonalizable, being of Jordan-block form. With PT symmetry we establish that conformal gravity is consistent at the quantum-mechanical level. In consequence, we can apply the theory to data, to find that the theory is capable of naturally accounting for the systematics of the rotation curves of a large and varied sample of 138 spiral galaxies without any need for dark matter. The success of the fits provides evidence for the relevance of non-diagonalizable but PT-symmetric Hamiltonians to physics. (Copyright copyright 2013 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Hamiltonian fluid closures of the Vlasov-Ampère equations: From water-bags to N moment models

Energy Technology Data Exchange (ETDEWEB)

Perin, M.; Chandre, C.; Tassi, E. [Aix-Marseille Université, Université de Toulon, CNRS, CPT UMR 7332, 13288 Marseille (France); Morrison, P. J. [Department of Physics and Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712-1060 (United States)

2015-09-15

Moment closures of the Vlasov-Ampère system, whereby higher moments are represented as functions of lower moments with the constraint that the resulting fluid system remains Hamiltonian, are investigated by using water-bag theory. The link between the water-bag formalism and fluid models that involve density, fluid velocity, pressure and higher moments is established by introducing suitable thermodynamic variables. The cases of one, two, and three water-bags are treated and their Hamiltonian structures are provided. In each case, we give the associated fluid closures and we discuss their Casimir invariants. We show how the method can be extended to an arbitrary number of fields, i.e., an arbitrary number of water-bags and associated moments. The thermodynamic interpretation of the resulting models is discussed. Finally, a general procedure to derive Hamiltonian N-field fluid models is proposed.

Quadratic hamiltonians and relativistic quantum mechanics

International Nuclear Information System (INIS)

Razumov, A.V.; Solov'ev, V.O.; Taranov, A.Yu.

1981-01-01

For the case of a charged scalar field described by a quadratic hamiltonian the equivalent relativistic quantum mechanics is constructed in one-particle sector. Complete investigation of a charged relativistic particle motion in the Coulomb field is carried out. Subcritical as well as supercritical cases are considered. In the course of investigation of the charged scalar particle in the Coulomb field the diagonalization of the quadratic hamiltonian describing the charged scalar quantized field interaction with the external Coulomb field has taken place. Mathematically this problem is bound to the construction of self-conjugated expansions of the symmetric operator. The construction of such expansion is necessary at any small external field magnitude [ru

Quasiperiodical orbits in the scalar classical lambdaphi4 field theory

International Nuclear Information System (INIS)

Belova, T.I.; Kudryavtsev, A.E.

1985-01-01

New numerical and theoretical results of resonance kink-antikink (Kanti K) interactions in the classical one-dimentional space Higgs theory are presented. Earlier studies of these interactions revealed nine initial relative velocity-intervals with two-bounce Kanti K-collisions followed by the escape of kinks to infinite separations, the breathing solution was formed outside those intervals. Two-bounce Kanti K-interactions with the number of small oscillations between Kanti K-bounces up to 35 in the initial kink velocity interval 0.18 <= Vsub(infinite) <= 0.26 were found. Several examples for n-bounces Kanti K-interaction (n <= 6) are also found. The observed phenomenon can be explaned by the existence of quasi-two-periodical solutions of the nonlinear wave equation. The simple Hamiltonian with two degrees of freedom is studied. This model supplies quantitative descrtiptions of all numerical results for the field theory considered above. The considered phenomenon may be called ''autoquantization'' of a nonlinear classical scalar selfinteracting field

Nonrelativistic Conformed Symmetry in 2 + 1 Dimensional Field Theory.

Science.gov (United States)

Bergman, Oren

This thesis is devoted to the study of conformal invariance and its breaking in non-relativistic field theories. It is a well known feature of relativistic field theory that theories which are conformally invariant at the classical level can acquire a conformal anomaly upon quantization and renormalization. The anomaly appears through the introduction of an arbitrary, but dimensionful, renormalization scale. One does not usually associate the concepts of renormalization and anomaly with nonrelativistic quantum mechanics, but there are a few examples where these concepts are useful. The most well known case is the two-dimensional delta -function potential. In two dimensions the delta-function scales like the kinetic term of the Hamiltonian, and therefore the problem is classically conformally invariant. Another example of classical conformal invariance is the famous Aharonov-Bohm (AB) problem. In that case each partial wave sees a 1/r^2 potential. We use the second quantized formulation of these problems, namely the nonrelativistic field theories, to compute Green's functions and derive the conformal anomaly. In the case of the AB problem we also solve an old puzzle, namely how to reproduce the result of Aharonov and Bohm in perturbation theory. The thesis is organized in the following manner. Chapter 1 is an introduction to nonrelativistic field theory, nonrelativistic conformal invariance, contact interactions and the AB problem. In Chapter 2 we discuss nonrelativistic scalar field theory, and how its quantization produces the anomaly. Chapter 3 is devoted to the AB problem, and the resolution of the perturbation puzzle. In Chapter 4 we generalize the discussion of Chapter 3 to particles carrying nonabelian charges. The structure of the nonabelian theory is much richer, and deserves a separate discussion. We also comment on the issues of forward scattering and single -valuedness of wavefunctions, which are important for Chapter 3 as well. (Copies available

Quantum Hamiltonian Physics with Supercomputers

International Nuclear Information System (INIS)

Vary, James P.

2014-01-01

The vision of solving the nuclear many-body problem in a Hamiltonian framework with fundamental interactions tied to QCD via Chiral Perturbation Theory is gaining support. The goals are to preserve the predictive power of the underlying theory, to test fundamental symmetries with the nucleus as laboratory and to develop new understandings of the full range of complex quantum phenomena. Advances in theoretical frameworks (renormalization and many-body methods) as well as in computational resources (new algorithms and leadership-class parallel computers) signal a new generation of theory and simulations that will yield profound insights into the origins of nuclear shell structure, collective phenomena and complex reaction dynamics. Fundamental discovery opportunities also exist in such areas as physics beyond the Standard Model of Elementary Particles, the transition between hadronic and quark–gluon dominated dynamics in nuclei and signals that characterize dark matter. I will review some recent achievements and present ambitious consensus plans along with their challenges for a coming decade of research that will build new links between theory, simulations and experiment. Opportunities for graduate students to embark upon careers in the fast developing field of supercomputer simulations is also discussed

Quantum Hamiltonian Physics with Supercomputers

Energy Technology Data Exchange (ETDEWEB)

Vary, James P.

2014-06-15

The vision of solving the nuclear many-body problem in a Hamiltonian framework with fundamental interactions tied to QCD via Chiral Perturbation Theory is gaining support. The goals are to preserve the predictive power of the underlying theory, to test fundamental symmetries with the nucleus as laboratory and to develop new understandings of the full range of complex quantum phenomena. Advances in theoretical frameworks (renormalization and many-body methods) as well as in computational resources (new algorithms and leadership-class parallel computers) signal a new generation of theory and simulations that will yield profound insights into the origins of nuclear shell structure, collective phenomena and complex reaction dynamics. Fundamental discovery opportunities also exist in such areas as physics beyond the Standard Model of Elementary Particles, the transition between hadronic and quark–gluon dominated dynamics in nuclei and signals that characterize dark matter. I will review some recent achievements and present ambitious consensus plans along with their challenges for a coming decade of research that will build new links between theory, simulations and experiment. Opportunities for graduate students to embark upon careers in the fast developing field of supercomputer simulations is also discussed.

Perspective: Quantum Hamiltonians for optical interactions

Science.gov (United States)

Andrews, David L.; Jones, Garth A.; Salam, A.; Woolley, R. Guy

2018-01-01

The multipolar Hamiltonian of quantum electrodynamics is extensively employed in chemical and optical physics to treat rigorously the interaction of electromagnetic fields with matter. It is also widely used to evaluate intermolecular interactions. The multipolar version of the Hamiltonian is commonly obtained by carrying out a unitary transformation of the Coulomb gauge Hamiltonian that goes by the name of Power-Zienau-Woolley (PZW). Not only does the formulation provide excellent agreement with experiment, and versatility in its predictive ability, but also superior physical insight. Recently, the foundations and validity of the PZW Hamiltonian have been questioned, raising a concern over issues of gauge transformation and invariance, and whether observable quantities obtained from unitarily equivalent Hamiltonians are identical. Here, an in-depth analysis of theoretical foundations clarifies the issues and enables misconceptions to be identified. Claims of non-physicality are refuted: the PZW transformation and ensuing Hamiltonian are shown to rest on solid physical principles and secure theoretical ground.

Optimal adaptive control for quantum metrology with time-dependent Hamiltonians

Science.gov (United States)

Pang, Shengshi; Jordan, Andrew N.

2017-01-01

Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, due to the complexity of dynamics, little has been known about quantum metrology. Here we investigate quantum metrology with time-dependent Hamiltonians to bridge this gap. We obtain the optimal quantum Fisher information for parameters in time-dependent Hamiltonians, and show proper Hamiltonian control is generally necessary to optimize the Fisher information. We derive the optimal Hamiltonian control, which is generally adaptive, and the measurement scheme to attain the optimal Fisher information. In a minimal example of a qubit in a rotating magnetic field, we find a surprising result that the fundamental limit of T2 time scaling of quantum Fisher information can be broken with time-dependent Hamiltonians, which reaches T4 in estimating the rotation frequency of the field. We conclude by considering level crossings in the derivatives of the Hamiltonians, and point out additional control is necessary for that case. PMID:28276428

Optimal adaptive control for quantum metrology with time-dependent Hamiltonians.

Science.gov (United States)

Pang, Shengshi; Jordan, Andrew N

2017-03-09

Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, due to the complexity of dynamics, little has been known about quantum metrology. Here we investigate quantum metrology with time-dependent Hamiltonians to bridge this gap. We obtain the optimal quantum Fisher information for parameters in time-dependent Hamiltonians, and show proper Hamiltonian control is generally necessary to optimize the Fisher information. We derive the optimal Hamiltonian control, which is generally adaptive, and the measurement scheme to attain the optimal Fisher information. In a minimal example of a qubit in a rotating magnetic field, we find a surprising result that the fundamental limit of T 2 time scaling of quantum Fisher information can be broken with time-dependent Hamiltonians, which reaches T 4 in estimating the rotation frequency of the field. We conclude by considering level crossings in the derivatives of the Hamiltonians, and point out additional control is necessary for that case.

Hamiltonian Cycles on Random Eulerian Triangulations

DEFF Research Database (Denmark)

Guitter, E.; Kristjansen, C.; Nielsen, Jakob Langgaard

1998-01-01

. Considering the case n -> 0, this implies that the system of random Eulerian triangulations equipped with Hamiltonian cycles describes a c=-1 matter field coupled to 2D quantum gravity as opposed to the system of usual random triangulations equipped with Hamiltonian cycles which has c=-2. Hence, in this case...

Lagrangian and Hamiltonian structures in an integrable hierarchy and space–time duality

International Nuclear Information System (INIS)

Avan, Jean; Caudrelier, Vincent; Doikou, Anastasia; Kundu, Anjan

2016-01-01

We define and illustrate the novel notion of dual integrable hierarchies, on the example of the nonlinear Schrödinger (NLS) hierarchy. For each integrable nonlinear evolution equation (NLEE) in the hierarchy, dual integrable structures are characterized by the fact that the zero-curvature representation of the NLEE can be realized by two Hamiltonian formulations stemming from two distinct choices of the configuration space, yielding two inequivalent Poisson structures on the corresponding phase space and two distinct Hamiltonians. This is fundamentally different from the standard bi-Hamiltonian or generally multitime structure. The first formulation chooses purely space-dependent fields as configuration space; it yields the standard Poisson structure for NLS. The other one is new: it chooses purely time-dependent fields as configuration space and yields a different Poisson structure at each level of the hierarchy. The corresponding NLEE becomes a space evolution equation. We emphasize the role of the Lagrangian formulation as a unifying framework for deriving both Poisson structures, using ideas from covariant field theory. One of our main results is to show that the two matrices of the Lax pair satisfy the same form of ultralocal Poisson algebra (up to a sign) characterized by an r-matrix structure, whereas traditionally only one of them is involved in the classical r-matrix method. We construct explicit dual hierarchies of Hamiltonians, and Lax representations of the triggered dynamics, from the monodromy matrices of either Lax matrix. An appealing procedure to build a multi-dimensional lattice of Lax pair, through successive uses of the dual Poisson structures, is briefly introduced.

Lagrangian and Hamiltonian structures in an integrable hierarchy and space–time duality

Energy Technology Data Exchange (ETDEWEB)

Avan, Jean, E-mail: Jean.Avan@u-cergy.fr [Laboratoire de Physique Théorique et Modélisation (CNRS UMR 8089), Université de Cergy-Pontoise, F-95302 Cergy-Pontoise (France); Caudrelier, Vincent, E-mail: v.caudrelier@city.ac.uk [Department of Mathematics, City University London, Northampton Square, EC1V 0HB London (United Kingdom); Doikou, Anastasia, E-mail: A.Doikou@hw.ac.uk [Department of Mathematics, Heriot-Watt University, EH14 4AS, Edinburgh (United Kingdom); Kundu, Anjan, E-mail: Anjan.Kundu@saha.ac.in [Saha Institute of Nuclear Physics, Theory Division, Kolkata (India)

2016-01-15

We define and illustrate the novel notion of dual integrable hierarchies, on the example of the nonlinear Schrödinger (NLS) hierarchy. For each integrable nonlinear evolution equation (NLEE) in the hierarchy, dual integrable structures are characterized by the fact that the zero-curvature representation of the NLEE can be realized by two Hamiltonian formulations stemming from two distinct choices of the configuration space, yielding two inequivalent Poisson structures on the corresponding phase space and two distinct Hamiltonians. This is fundamentally different from the standard bi-Hamiltonian or generally multitime structure. The first formulation chooses purely space-dependent fields as configuration space; it yields the standard Poisson structure for NLS. The other one is new: it chooses purely time-dependent fields as configuration space and yields a different Poisson structure at each level of the hierarchy. The corresponding NLEE becomes a space evolution equation. We emphasize the role of the Lagrangian formulation as a unifying framework for deriving both Poisson structures, using ideas from covariant field theory. One of our main results is to show that the two matrices of the Lax pair satisfy the same form of ultralocal Poisson algebra (up to a sign) characterized by an r-matrix structure, whereas traditionally only one of them is involved in the classical r-matrix method. We construct explicit dual hierarchies of Hamiltonians, and Lax representations of the triggered dynamics, from the monodromy matrices of either Lax matrix. An appealing procedure to build a multi-dimensional lattice of Lax pair, through successive uses of the dual Poisson structures, is briefly introduced.

Quantum Hamiltonian reduction in superspace formalism

International Nuclear Information System (INIS)

Madsen, J.O.; Ragoucy, E.

1994-02-01

Recently the quantum Hamiltonian reduction was done in the case of general sl(2) embeddings into Lie algebras and superalgebras. The results are extended to the quantum Hamiltonian reduction of N=1 affine Lie superalgebras in the superspace formalism. It is shown that if we choose a gauge for the supersymmetry, and consider only certain equivalence classes of fields, then our quantum Hamiltonian reduction reduces to quantum Hamiltonian reduction of non-supersymmetric Lie superalgebras. The super energy-momentum tensor is constructed explicitly as well as all generators of spin 1 (and 1/2); thus all generators in the superconformal, quasi-superconformal and Z 2 *Z 2 superconformal algebras are constructed. (authors). 21 refs

Generalized internal long wave equations: construction, hamiltonian structure and conservation laws

International Nuclear Information System (INIS)

Lebedev, D.R.

1982-01-01

Some aspects of the theory of the internal long-wave equations (ILW) are considered. A general class of the ILW type equations is constructed by means of the Zakharov-Shabat ''dressing'' method. Hamiltonian structure and infinite numbers of conservation laws are introduced. The considered equations are shown to be Hamiltonian in the so-called second Hamiltonian structu

Alternative Hamiltonian representation for gravity

International Nuclear Information System (INIS)

Rosas-RodrIguez, R

2007-01-01

By using a Hamiltonian formalism for fields wider than the canonical one, we write the Einstein vacuum field equations in terms of alternative variables. This variables emerge from the Ashtekar's formalism for gravity

Theoretical calculations of spin-Hamiltonian parameters for the rhombic-like Mo5+ centers in KTiOPO4 crystal

International Nuclear Information System (INIS)

Yang, Mei; Wen-Chen, Zheng; Hong-Gang, Liu

2013-01-01

The spin-Hamiltonian parameters (g factors g i and hyperfine structure constants A i , were i=x, y and z) for Mo 5+ ion occupying the Ti(1) site with approximately rhombic symmetry in KTiOPO 4 crystal are calculated from the high-order perturbation formulas based on the two-mechanism model. In the model, not only the contribution due to the conventional crystal-field (CF) mechanism, but also those due to the charge-transfer (CT) mechanism are included. The six calculated spin-Hamiltonian parameters with four adjustable parameters are in reasonable agreement with the experimental values. The calculations show that for more accurate calculations of spin-Hamiltonian parameters of the high valence d n ions (e.g., Mo 5+ considered here) in crystals, the contribution from CT mechanism, which is ignored in the conventional crystal field theory, should be taken into account. The reasonable crystal field energy levels of Mo 5+ in KTiOPO 4 are also predicted from calculations

Phase transitions in the Hubbard Hamiltonian

International Nuclear Information System (INIS)

Chaves, C.M.; Lederer, P.; Gomes, A.A.

1977-05-01

Phase transition in the isotropic non-degenerate Hubbard Hamiltonian within the renormalization group techniques is studied, using the epsilon = 4 - d expansion to first order in epsilon. The functional obtained from the Hubbard Hamiltonian displays full rotation symmetry and describes two coupled fields: a vector spin field, with n components and a non-soft scalar charge field. This coupling is pure imaginary, which has interesting consequences on the critical properties of this coupled field system. The effect of simple constraints imposed on the charge field is considered. The relevance of the coupling between the fields in producing Fisher renormalization of the critical exponents is discussed. The possible singularities introduced in the charge-charge correlation function by the coupling are also discussed

An introduction to topological Yang-Mills theory

International Nuclear Information System (INIS)

Baal, P. van; Rijksuniversiteit Utrecht

1990-01-01

In these lecture notes I give a ''historical'' introduction to topological gauge theories. My main aim is to clearly explain the origin of the Hamiltonian which forms the basis of Witten's construction of topological gauge theory. I show how this Hamiltonian arises from Witten's formulation of Morse theory as applied by Floer to the infinite dimensional space of gauge connections, with the Chern-Simons functional as the appriopriate Morse function(al). I therefore discuss the De Rham cohomology, Hodge theory, Morse theory, Floer homology, Witten's construction of the Lagrangian for topological gauge theory, the subsequent BRST formulation of topological quantum field theory and finally Witten's construction of the Donaldson polynomials. (author)

On quantization of supersymmetric theories

International Nuclear Information System (INIS)

Smilga, A.V.

1985-01-01

A recipe to resolve ordering ambiguities in the quantum hamiltonian of supersymmetric theories is suggested. The Weyl ordering prescription for supercharge operators should be employed to preserve SUSY algebra on the quantum level. The quantum hamiltonian does not generally coincide with the Weyl ordered classical hamiltonian, the difference being due to the fact that the Weyl symbol of anticommutator of supercharges does not generally coincide with the Poisson bracket of their Weyl symbols (i.e. the classical hamiltonian). The suggested procedure is applied in the examples of N=1 and N=2 supersymmetric σ-models analyzed in the constant field limit

Nonperturbative loop quantization of scalar-tensor theories of gravity

International Nuclear Information System (INIS)

Zhang Xiangdong; Ma Yongge

2011-01-01

The Hamiltonian formulation of scalar-tensor theories of gravity is derived from their Lagrangian formulation by Hamiltonian analysis. The Hamiltonian formalism marks off two sectors of the theories by the coupling parameter ω(φ). In the sector of ω(φ)=-(3/2), the feasible theories are restricted and a new primary constraint generating conformal transformations of spacetime is obtained, while in the other sector of ω(φ)≠-(3/2), the canonical structure and constraint algebra of the theories are similar to those of general relativity coupled with a scalar field. By canonical transformations, we further obtain the connection-dynamical formalism of the scalar-tensor theories with real su(2) connections as configuration variables in both sectors. This formalism enables us to extend the scheme of nonperturbative loop quantum gravity to the scalar-tensor theories. The quantum kinematical framework for the scalar-tensor theories is rigorously constructed. Both the Hamiltonian constraint operator and master constraint operator are well defined and proposed to represent quantum dynamics. Thus the loop quantum gravity method is also valid for general scalar-tensor theories.

Alternative Hamiltonian representation for gravity

Energy Technology Data Exchange (ETDEWEB)

Rosas-RodrIguez, R [Instituto de Fisica, Universidad Autonoma de Puebla, Apdo. Postal J-48, 72570, Puebla, Pue. (Mexico)

2007-11-15

By using a Hamiltonian formalism for fields wider than the canonical one, we write the Einstein vacuum field equations in terms of alternative variables. This variables emerge from the Ashtekar's formalism for gravity.

The intrinsic stochasticity of near-integrable Hamiltonian systems

Energy Technology Data Exchange (ETDEWEB)

Krlin, L [Ceskoslovenska Akademie Ved, Prague (Czechoslovakia). Ustav Fyziky Plazmatu

1989-09-01

Under certain conditions, the dynamics of near-integrable Hamiltonian systems appears to be stochastic. This stochasticity (intrinsic stochasticity, or deterministic chaos) is closely related to the Kolmogorov-Arnold-Moser (KAM) theorem of the stability of near-integrable multiperiodic Hamiltonian systems. The effect of the intrinsic stochasticity attracts still growing attention both in theory and in various applications in contemporary physics. The paper discusses the relation of the intrinsic stochasticity to the modern ergodic theory and to the KAM theorem, and describes some numerical experiments on related astrophysical and high-temperature plasma problems. Some open questions are mentioned in conclusion. (author).

The detectability lemma and its applications to quantum Hamiltonian complexity

International Nuclear Information System (INIS)

Aharonov, Dorit; Arad, Itai; Vazirani, Umesh; Landau, Zeph

2011-01-01

Quantum Hamiltonian complexity, an emerging area at the intersection of condensed matter physics and quantum complexity theory, studies the properties of local Hamiltonians and their ground states. In this paper we focus on a seemingly specialized technical tool, the detectability lemma (DL), introduced in the context of the quantum PCP challenge (Aharonov et al 2009 arXiv:0811.3412), which is a major open question in quantum Hamiltonian complexity. We show that a reformulated version of the lemma is a versatile tool that can be used in place of the celebrated Lieb-Robinson (LR) bound to prove several important results in quantum Hamiltonian complexity. The resulting proofs are much simpler, more combinatorial and provide a plausible path toward tackling some fundamental open questions in Hamiltonian complexity. We provide an alternative simpler proof of the DL that removes a key restriction in the original statement (Aharonov et al 2009 arXiv:0811.3412), making it more suitable for the broader context of quantum Hamiltonian complexity. Specifically, we first use the DL to provide a one-page proof of Hastings' result that the correlations in the ground states of gapped Hamiltonians decay exponentially with distance (Hastings 2004 Phys. Rev. B 69 104431). We then apply the DL to derive a simpler and more intuitive proof of Hastings' seminal one-dimensional (1D) area law (Hastings 2007 J. Stat. Mech. (2007) P8024) (both these proofs are restricted to frustration-free systems). Proving the area law for two and higher dimensions is one of the most important open questions in the field of Hamiltonian complexity, and the combinatorial nature of the DL-based proof holds out hope for a possible generalization. Indeed, soon after the first publication of the methods presented here, they were applied to derive exponential improvements to Hastings' result (Arad et al 2011, Aharonov et al 2011) in the case of frustration-free 1D systems. Finally, we also provide a more general

Some studies of the relativistic theories for spin-3/2 particles and its interactions with an uniforme magnetic field

International Nuclear Information System (INIS)

Oliveira, M.A.B. de.

1984-01-01

We present our investigations on the problems of non-causality of propagation, at the c-number level, of four spin 3/2 theories in the Schroedinger form employing the minimum number of eight components, in interaction with a constant magnetic field. Analyzing first the basic formulations of free particle spin 3/2 relativistic wave equations, we deduze, extending to spin 3/2 Dirac's ''spin 1/2 factorization'' of the mas condition, a new eight-component relativistic wave equation in the Schroedinger form for this spin and prove its relativistic invariance. We demostrate explicitly that the entire content of the Rarita-Schwinger (RS) theory for spin 3/2 can be written in the form of two Dirac-Like wave equations. We demonstrate that our wave equation for spin 3/2 cab indeed be deduzed from a modified RS theory wherein both Hamiltonians above referred to are taken hermitian. We also establish, in a transparent maner, the equivalences existing between the formalisms of RS, Belinfante and Hurley-Sudarshan for spin 3/2. We investigate the c-number problem of the stationary state eigevalues of the spin 3/2 Hamiltonians in a constant external magnetic field, in the four theories in the Schoedinger form with eight components, those of Moldauer and Case (deduzed from TS theory), of Weaver, Hammer and Good. (autor) [pt

Hamiltonian analysis for linearly acceleration-dependent Lagrangians

Energy Technology Data Exchange (ETDEWEB)

Cruz, Miguel, E-mail: miguelcruz02@uv.mx, E-mail: roussjgc@gmail.com, E-mail: molgado@fc.uaslp.mx, E-mail: efrojas@uv.mx; Gómez-Cortés, Rosario, E-mail: miguelcruz02@uv.mx, E-mail: roussjgc@gmail.com, E-mail: molgado@fc.uaslp.mx, E-mail: efrojas@uv.mx; Rojas, Efraín, E-mail: miguelcruz02@uv.mx, E-mail: roussjgc@gmail.com, E-mail: molgado@fc.uaslp.mx, E-mail: efrojas@uv.mx [Facultad de Física, Universidad Veracruzana, 91000 Xalapa, Veracruz, México (Mexico); Molgado, Alberto, E-mail: miguelcruz02@uv.mx, E-mail: roussjgc@gmail.com, E-mail: molgado@fc.uaslp.mx, E-mail: efrojas@uv.mx [Facultad de Ciencias, Universidad Autónoma de San Luis Potosí, Avenida Salvador Nava S/N Zona Universitaria, CP 78290 San Luis Potosí, SLP, México (Mexico)

2016-06-15

We study the constrained Ostrogradski-Hamilton framework for the equations of motion provided by mechanical systems described by second-order derivative actions with a linear dependence in the accelerations. We stress out the peculiar features provided by the surface terms arising for this type of theories and we discuss some important properties for this kind of actions in order to pave the way for the construction of a well defined quantum counterpart by means of canonical methods. In particular, we analyse in detail the constraint structure for these theories and its relation to the inherent conserved quantities where the associated energies together with a Noether charge may be identified. The constraint structure is fully analyzed without the introduction of auxiliary variables, as proposed in recent works involving higher order Lagrangians. Finally, we also provide some examples where our approach is explicitly applied and emphasize the way in which our original arrangement results in propitious for the Hamiltonian formulation of covariant field theories.

Passivation controller design for turbo-generators based on generalised Hamiltonian system theory

NARCIS (Netherlands)

Cao, M.; Shen, T.L.; Song, Y.H.

2002-01-01

A method of pre-feedback to formulate the generalised forced Hamiltonian system model for speed governor control systems is proposed. Furthermore, passivation controllers are designed based on the scheme of Hamiltonian structure for single machne infinite bus and multimachine power systems. In

Construction of Hamiltonians by supervised learning of energy and entanglement spectra

Science.gov (United States)

Fujita, Hiroyuki; Nakagawa, Yuya O.; Sugiura, Sho; Oshikawa, Masaki

2018-02-01

Correlated many-body problems ubiquitously appear in various fields of physics such as condensed matter, nuclear, and statistical physics. However, due to the interplay of the large number of degrees of freedom, it is generically impossible to treat these problems from first principles. Thus the construction of a proper model, namely, effective Hamiltonian, is essential. Here, we propose a simple supervised learning algorithm for constructing Hamiltonians from given energy or entanglement spectra. We apply the proposed scheme to the Hubbard model at the half-filling, and compare the obtained effective low-energy spin model with several analytic results based on the high-order perturbation theory, which have been inconsistent with each other. We also show that our approach can be used to construct the entanglement Hamiltonian of a quantum many-body state from its entanglement spectrum as well. We exemplify this using the ground states of the S =1 /2 two-leg Heisenberg ladders. We observe a qualitative difference between the entanglement Hamiltonians of the two phases (the Haldane and the rung singlet phase) of the model due to the different origin of the entanglement. In the Haldane phase, we find that the entanglement Hamiltonian is nonlocal by nature, and the locality can be restored by introducing the anisotropy and turning the ground state into the large-D phase. Possible applications to the model construction from experimental data and to various problems of strongly correlated systems are discussed.

Intertwined Hamiltonians in two-dimensional curved spaces

International Nuclear Information System (INIS)

Aghababaei Samani, Keivan; Zarei, Mina

2005-01-01

The problem of intertwined Hamiltonians in two-dimensional curved spaces is investigated. Explicit results are obtained for Euclidean plane, Minkowski plane, Poincare half plane (AdS 2 ), de Sitter plane (dS 2 ), sphere, and torus. It is shown that the intertwining operator is related to the Killing vector fields and the isometry group of corresponding space. It is shown that the intertwined potentials are closely connected to the integral curves of the Killing vector fields. Two problems are considered as applications of the formalism presented in the paper. The first one is the problem of Hamiltonians with equispaced energy levels and the second one is the problem of Hamiltonians whose spectrum is like the spectrum of a free particle

Variational derivation of a time-dependent Hartree-Fock Hamiltonian

International Nuclear Information System (INIS)

Lichtner, P.C.; Griffin, J.J.; Schultheis, H.; Schultheis, R.; Volkov, A.B.

1979-01-01

The variational derivation of the time-dependent Hartree-Fock equation is reviewed. When norm-violating variations are included, a unique time-dependent Hartree-Fock Hamiltonian, which differs from that customarily used in time-dependent Hartree-Fock analyses, is implied. This variationally ''true'' Hartree-Fock Hamiltonian has the same expectation value as the exact Hamiltonian, equal to the average energy of the system. Since this quantity remains constant under time-dependent Hartree-Fock time evolution, we suggest the label ''constant '' for this form of time-dependent Hartree-Fock theory

Schrödinger Theory of Electrons in Electromagnetic Fields: New Perspectives

Directory of Open Access Journals (Sweden)

Viraht Sahni

2017-03-01

Full Text Available The Schrödinger theory of electrons in an external electromagnetic field is described from the new perspective of the individual electron. The perspective is arrived at via the time-dependent “Quantal Newtonian” law (or differential virial theorem. (The time-independent law, a special case, provides a similar description of stationary-state theory. These laws are in terms of “classical” fields whose sources are quantal expectations of Hermitian operators taken with respect to the wave function. The laws reveal the following physics: (a in addition to the external field, each electron experiences an internal field whose components are representative of a specific property of the system such as the correlations due to the Pauli exclusion principle and Coulomb repulsion, the electron density, kinetic effects, and an internal magnetic field component. The response of the electron is described by the current density field; (b the scalar potential energy of an electron is the work done in a conservative field. It is thus path-independent. The conservative field is the sum of the internal and Lorentz fields. Hence, the potential is inherently related to the properties of the system, and its constituent property-related components known. As the sources of the fields are functionals of the wave function, so are the respective fields, and, therefore, the scalar potential is a known functional of the wave function; (c as such, the system Hamiltonian is a known functional of the wave function. This reveals the intrinsic self-consistent nature of the Schrödinger equation, thereby providing a path for the determination of the exact wave functions and energies of the system; (d with the Schrödinger equation written in self-consistent form, the Hamiltonian now admits via the Lorentz field a new term that explicitly involves the external magnetic field. The new understandings are explicated for the stationary state case by application to two quantum

Landau-like theory for universality of critical exponents in quasistationary states of isolated mean-field systems.

Science.gov (United States)

Ogawa, Shun; Yamaguchi, Yoshiyuki Y

2015-06-01

An external force dynamically drives an isolated mean-field Hamiltonian system to a long-lasting quasistationary state, whose lifetime increases with population of the system. For second order phase transitions in quasistationary states, two nonclassical critical exponents have been reported individually by using a linear and a nonlinear response theories in a toy model. We provide a simple way to compute the critical exponents all at once, which is an analog of the Landau theory. The present theory extends the universality class of the nonclassical exponents to spatially periodic one-dimensional systems and shows that the exponents satisfy a classical scaling relation inevitably by using a key scaling of momentum.

Hamiltonian PDEs and Frobenius manifolds

International Nuclear Information System (INIS)

Dubrovin, Boris A

2008-01-01

In the first part of this paper the theory of Frobenius manifolds is applied to the problem of classification of Hamiltonian systems of partial differential equations depending on a small parameter. Also developed is a deformation theory of integrable hierarchies including the subclass of integrable hierarchies of topological type. Many well-known examples of integrable hierarchies, such as the Korteweg-de Vries, non-linear Schroedinger, Toda, Boussinesq equations, and so on, belong to this subclass that also contains new integrable hierarchies. Some of these new integrable hierarchies may be important for applications. Properties of the solutions to these equations are studied in the second part. Consideration is given to the comparative study of the local properties of perturbed and unperturbed solutions near a point of gradient catastrophe. A Universality Conjecture is formulated describing the various types of critical behaviour of solutions to perturbed Hamiltonian systems near the point of gradient catastrophe of the unperturbed solution.

Hamiltonian PDEs and Frobenius manifolds

Energy Technology Data Exchange (ETDEWEB)

Dubrovin, Boris A [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)

2008-12-31

In the first part of this paper the theory of Frobenius manifolds is applied to the problem of classification of Hamiltonian systems of partial differential equations depending on a small parameter. Also developed is a deformation theory of integrable hierarchies including the subclass of integrable hierarchies of topological type. Many well-known examples of integrable hierarchies, such as the Korteweg-de Vries, non-linear Schroedinger, Toda, Boussinesq equations, and so on, belong to this subclass that also contains new integrable hierarchies. Some of these new integrable hierarchies may be important for applications. Properties of the solutions to these equations are studied in the second part. Consideration is given to the comparative study of the local properties of perturbed and unperturbed solutions near a point of gradient catastrophe. A Universality Conjecture is formulated describing the various types of critical behaviour of solutions to perturbed Hamiltonian systems near the point of gradient catastrophe of the unperturbed solution.

A Hamiltonian approach to Thermodynamics

Energy Technology Data Exchange (ETDEWEB)

Baldiotti, M.C., E-mail: baldiotti@uel.br [Departamento de Física, Universidade Estadual de Londrina, 86051-990, Londrina-PR (Brazil); Fresneda, R., E-mail: rodrigo.fresneda@ufabc.edu.br [Universidade Federal do ABC, Av. dos Estados 5001, 09210-580, Santo André-SP (Brazil); Molina, C., E-mail: cmolina@usp.br [Escola de Artes, Ciências e Humanidades, Universidade de São Paulo, Av. Arlindo Bettio 1000, CEP 03828-000, São Paulo-SP (Brazil)

2016-10-15

In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed on top of a usual symplectic manifold, where phase space is even dimensional and one has well-defined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac’s theory of constrained systems is extensively used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases. - Highlights: • A strictly Hamiltonian approach to Thermodynamics is proposed. • Dirac’s theory of constrained systems is extensively used. • Thermodynamic equations of state are realized as constraints. • Thermodynamic potentials are related by canonical transformations.

A Hamiltonian approach to Thermodynamics

International Nuclear Information System (INIS)

Baldiotti, M.C.; Fresneda, R.; Molina, C.

2016-01-01

In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed on top of a usual symplectic manifold, where phase space is even dimensional and one has well-defined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac’s theory of constrained systems is extensively used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases. - Highlights: • A strictly Hamiltonian approach to Thermodynamics is proposed. • Dirac’s theory of constrained systems is extensively used. • Thermodynamic equations of state are realized as constraints. • Thermodynamic potentials are related by canonical transformations.

On bounded and unbounded dynamics of the Hamiltonian system for unified scalar field cosmology

International Nuclear Information System (INIS)

Starkov, Konstantin E.

2016-01-01

This paper is devoted to the research of global dynamics for the Hamiltonian system formed by the unified scalar field cosmology. We prove that this system possesses only unbounded dynamics in the space of negative curvature. It is found the invariant domain filled only by unbounded dynamics for the space with positive curvature. Further, we construct a set of polytopes depending on the Hamiltonian level surface that contain all compact invariant sets. Besides, one invariant two dimensional plane is described. Finally, we establish nonchaoticity of dynamics in one special case. - Highlights: • Unbounded dynamics is stated in case of negative curvature. • Domain with unbounded dynamics is got in case of positive curvature. • Localization polytope for compact invariant sets is computed. • One two dimensional invariant plane is described. • Nonchaotic dynamics is stated in one special case.

On bounded and unbounded dynamics of the Hamiltonian system for unified scalar field cosmology

Energy Technology Data Exchange (ETDEWEB)

Starkov, Konstantin E., E-mail: kstarkov@ipn.mx

2016-05-27

This paper is devoted to the research of global dynamics for the Hamiltonian system formed by the unified scalar field cosmology. We prove that this system possesses only unbounded dynamics in the space of negative curvature. It is found the invariant domain filled only by unbounded dynamics for the space with positive curvature. Further, we construct a set of polytopes depending on the Hamiltonian level surface that contain all compact invariant sets. Besides, one invariant two dimensional plane is described. Finally, we establish nonchaoticity of dynamics in one special case. - Highlights: • Unbounded dynamics is stated in case of negative curvature. • Domain with unbounded dynamics is got in case of positive curvature. • Localization polytope for compact invariant sets is computed. • One two dimensional invariant plane is described. • Nonchaotic dynamics is stated in one special case.

Reggeon field theory for alpha (0)>1

CERN Document Server

Amati, Daniele; Le Bellac, M; Marchesini, G

1976-01-01

The asymptotic behaviour of the scattering amplitude is obtained when the pomeron has intercept alpha (0) larger than one. The reggeon field theory is studied by introducing a lattice in impact parameter space. Use is made of a previous result showing that asymptotically the dynamics is controlled at each lattice site ( alpha '=0 case) by a two-level structure. This leads to a non-Hermitean Hamiltonian expressed in terms of spin operators in which the intersite interaction term is proportional to the pomeron slope alpha '. The spectrum of such a system shows a degenerate ground state for alpha (0)> alpha /sub c/>or approximately=1 and a continuum with vanishing excitation gap at alpha (0)= alpha /sub c/. The vacuum does not change structure at the critical value. The criticality is shown by an order parameter which is given by the matrix element of a field operator between the vacuum and its degenerate companion. The nature of this critical phenomenon is better understood by continuously transforming the Hami...

Hamiltonian formulation for the Martin-Taylor model

International Nuclear Information System (INIS)

Vasconcelos, D.B.; Viana, R.L.

1993-01-01

Locally stochastic layer and its optimization are studied. In order to accomplish this task, it is employed a Hamiltonian formulation of magnetic field line flow with a subsequent application of Escande-Doveil renormalization method which have been extensively used to obtain accurate estimates of stochasticity thresholds in systems exhibiting Hamiltonian chaos. (author)

Hamiltonian structure of linearly extended Virasoro algebra

International Nuclear Information System (INIS)

Arakelyan, T.A.; Savvidi, G.K.

1991-01-01

The Hamiltonian structure of linearly extended Virasoro algebra which admits free bosonic field representation is described. An example of a non-trivial extension is found. The hierarchy of integrable non-linear equations corresponding to this Hamiltonian structure is constructed. This hierarchy admits the Lax representation by matrix Lax operator of second order

On time-dependent Hamiltonian realizations of planar and nonplanar systems

Science.gov (United States)

Esen, Oğul; Guha, Partha

2018-04-01

In this paper, we elucidate the key role played by the cosymplectic geometry in the theory of time dependent Hamiltonian systems in 2 D. We generalize the cosymplectic structures to time-dependent Nambu-Poisson Hamiltonian systems and corresponding Jacobi's last multiplier for 3 D systems. We illustrate our constructions with various examples.

Geometric perturbation theory and plasma physics

Energy Technology Data Exchange (ETDEWEB)

Omohundro, S.M.

1985-04-04

Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a question about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no ad hoc elements. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A new type of attractor is defined which attracts both forward and backward in time and is shown to occur in infinite-dimensional Hamiltonian systems with dissipative behavior. The theory of Smale horseshoes is applied to gyromotion in the neighborhood of a magnetic field reversal and the phenomenon of reinsertion in area-preserving horseshoes is introduced. The central limit theorem is proved by renormalization group techniques. A natural symplectic structure for thermodynamics is shown to arise asymptotically from the maximum entropy formalism.

Geometric perturbation theory and plasma physics

International Nuclear Information System (INIS)

Omohundro, S.M.

1985-01-01

Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a question about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no ad hoc elements. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A new type of attractor is defined which attracts both forward and backward in time and is shown to occur in infinite-dimensional Hamiltonian systems with dissipative behavior. The theory of Smale horseshoes is applied to gyromotion in the neighborhood of a magnetic field reversal and the phenomenon of reinsertion in area-preserving horseshoes is introduced. The central limit theorem is proved by renormalization group techniques. A natural symplectic structure for thermodynamics is shown to arise asymptotically from the maximum entropy formalism

Hamiltonian dynamics for complex food webs

Science.gov (United States)

Kozlov, Vladimir; Vakulenko, Sergey; Wennergren, Uno

2016-03-01

We investigate stability and dynamics of large ecological networks by introducing classical methods of dynamical system theory from physics, including Hamiltonian and averaging methods. Our analysis exploits the topological structure of the network, namely the existence of strongly connected nodes (hubs) in the networks. We reveal new relations between topology, interaction structure, and network dynamics. We describe mechanisms of catastrophic phenomena leading to sharp changes of dynamics and hence completely altering the ecosystem. We also show how these phenomena depend on the structure of interaction between species. We can conclude that a Hamiltonian structure of biological interactions leads to stability and large biodiversity.

A recipe for constructing frustration-free Hamiltonians with gauge and matter fields in one and two dimensions

Science.gov (United States)

Bernabé Ferreira, Miguel Jorge; Ibieta Jimenez, Juan Pablo; Padmanabhan, Pramod; Teôtonio Sobrinho, Paulo

2015-12-01

State sum constructions, such as Kuperberg’s algorithm, give partition functions of physical systems, like lattice gauge theories, in various dimensions by associating local tensors or weights with different parts of a closed triangulated manifold. Here we extend this construction by including matter fields to build partition functions in both two and three space-time dimensions. The matter fields introduce new weights to the vertices and they correspond to Potts spin configurations described by an {A}-module with an inner product. Performing this construction on a triangulated manifold with a boundary we obtain transfer matrices which are decomposed into a product of local operators acting on vertices, links and plaquettes. The vertex and plaquette operators are similar to the ones appearing in the quantum double models (QDMs) of Kitaev. The link operator couples the gauge and the matter fields, and it reduces to the usual interaction terms in known models such as {{{Z}}}2 gauge theory with matter fields. The transfer matrices lead to Hamiltonians that are frustration-free and are exactly solvable. According to the choice of the initial input, that of the gauge group and a matter module, we obtain interesting models which have a new kind of ground state degeneracy that depends on the number of equivalence classes in the matter module under gauge action. Some of the models have confined flux excitations in the bulk which become deconfined at the surface. These edge modes are protected by an energy gap provided by the link operator. These properties also appear in ‘confined Walker-Wang’ models which are 3D models having interesting surface states. Apart from the gauge excitations there are also excitations in the matter sector which are immobile and can be thought of as defects like in the Ising model. We only consider bosonic matter fields in this paper.

A few comments on general theory of quantized fields

International Nuclear Information System (INIS)

Yamaguchi, Yoshio

2005-01-01

Several important comments on General Theory of Quantized Fields shall be supplemented here. Our theory is based on (Riemannian) momentum spaces with finite volumes. Our theory is formulated in the specific inertial frame, i.e., the rest frame of the cosmic back-ground radiation (RF-CBR). To go to other reference frame, we reply on general co-ordinate (in our case, energy and momentum variables, p-representation) transformations and the principle of general relativity. We find the degeneracy on energy levels of all elementary particles (same values of all particle energies appear twice) (as compared to the conventional field theories). This doubling of energy levels might be important at the beginning (very early stage) of our evolutional universe. However, we may not wish to have such a doubling at the present epoch. We can avoid the doubling by introducing appropriate (natural and rational, of course) Yukawa interactions among fermions and bosons. Then it is easy to realize the situation in which elementary particles populated in the half of the energy levels (called 'our particles' having normal spin multiplicity) shall not 'interact' with particles populated in the other half of energy levels except gravity. The particles in the latter group may be called 'dark matter particles', which give the most natural candidates of dark matter. We have already emphasized that other candidates of dark matter are zero-point vibration energy of all elementary particles and the energy of the vacuum due to interaction Hamiltonians. (author)

Hamiltonian dynamics

CERN Document Server

Vilasi, Gaetano

2001-01-01

This is both a textbook and a monograph. It is partially based on a two-semester course, held by the author for third-year students in physics and mathematics at the University of Salerno, on analytical mechanics, differential geometry, symplectic manifolds and integrable systems. As a textbook, it provides a systematic and self-consistent formulation of Hamiltonian dynamics both in a rigorous coordinate language and in the modern language of differential geometry. It also presents powerful mathematical methods of theoretical physics, especially in gauge theories and general relativity. As a m

Unitary field theories

International Nuclear Information System (INIS)

Bergmann, P.G.

1980-01-01

A problem of construction of the unitary field theory is discussed. The preconditions of the theory are briefly described. The main attention is paid to the geometrical interpretation of physical fields. The meaning of the conceptions of diversity and exfoliation is elucidated. Two unitary field theories are described: the Weyl conformic geometry and Calitzy five-dimensioned theory. It is proposed to consider supersymmetrical theories as a new approach to the problem of a unitary field theory. It is noted that the supergravitational theories are really unitary theories, since the fields figuring there do not assume invariant expansion

Hierarchical theory of quantum adiabatic evolution

International Nuclear Information System (INIS)

Zhang, Qi; Wu, Biao; Gong, Jiangbin

2014-01-01

Quantum adiabatic evolution is a dynamical evolution of a quantum system under slow external driving. According to the quantum adiabatic theorem, no transitions occur between nondegenerate instantaneous energy eigenstates in such a dynamical evolution. However, this is true only when the driving rate is infinitesimally small. For a small nonzero driving rate, there are generally small transition probabilities between the energy eigenstates. We develop a classical mechanics framework to address the small deviations from the quantum adiabatic theorem order by order. A hierarchy of Hamiltonians is constructed iteratively with the zeroth-order Hamiltonian being determined by the original system Hamiltonian. The kth-order deviations are governed by a kth-order Hamiltonian, which depends on the time derivatives of the adiabatic parameters up to the kth-order. Two simple examples, the Landau–Zener model and a spin-1/2 particle in a rotating magnetic field, are used to illustrate our hierarchical theory. Our analysis also exposes a deep, previously unknown connection between classical adiabatic theory and quantum adiabatic theory. (paper)

H∞ Excitation Control Design for Stochastic Power Systems with Input Delay Based on Nonlinear Hamiltonian System Theory

Directory of Open Access Journals (Sweden)

Weiwei Sun

2015-01-01

Full Text Available This paper presents H∞ excitation control design problem for power systems with input time delay and disturbances by using nonlinear Hamiltonian system theory. The impact of time delays introduced by remote signal transmission and processing in wide-area measurement system (WAMS is well considered. Meanwhile, the systems under investigation are disturbed by random fluctuation. First, under prefeedback technique, the power systems are described as a nonlinear Hamiltonian system. Then the H∞ excitation controller of generators connected to distant power systems with time delay and stochasticity is designed. Based on Lyapunov functional method, some sufficient conditions are proposed to guarantee the rationality and validity of the proposed control law. The closed-loop systems under the control law are asymptotically stable in mean square independent of the time delay. And we through a simulation of a two-machine power system prove the effectiveness of the results proposed in this paper.

Phase transition in the non-degenerate Hubbard Hamiltonian

International Nuclear Information System (INIS)

Chaves, C.M.; Lederer, P.; Gomes, A.A.

1976-01-01

Phase transition in the isotropic non-degenerate Hubbard Hamiltonian within the renormalization group techniques, using the epsilon = 4 - d expansion to first order in epsilon, is studied. The functional obtained from the Hubbard Hamiltonian displays full rotation symmetry and describes two coupled fields: a vector spin field, with n components and a non-soft scalar charge field. The possibility of tricritical behavior then emerges. The effects of simple constraints imposed on the charge field is considered. The relevance of the coupling between the fields in producing Fisher renormalization of the critical exponents is discussed. The possible singularities introduced in the charge-charge correlation function by the coupling are also discussed

Nonlinear mean field theory for nuclear matter and surface properties

International Nuclear Information System (INIS)

Boguta, J.; Moszkowski, S.A.

1983-01-01

Nuclear matter properties are studied in a nonlinear relativistic mean field theory. We determine the parameters of the model from bulk properties of symmetric nuclear matter and a reasonable value of the effective mass. In this work, we stress the nonrelativistic limit of the theory which is essentially equivalent to a Skyrme hamiltonian, and we show that most of the results can be obtained, to a good approximation, analytically. The strength of the required parameters is determined from the binding energy and density of nuclear matter and the effective nucleon mass. For realistic values of the parameters, the nonrelativistic approximation turns out to be quite satisfactory. Using reasonable values of the parameters, we can account for other key properties of nuclei, such as the spin-orbit coupling, surface energy, and diffuseness of the nuclear surface. Also the energy dependence of the nucleon-nucleus optical model is accounted for reasonably well except near the Fermi surface. It is found, in agreement with empirical results, that the Landau parameter F 0 is quite small in normal nuclear matter. Both density dependence and momentum dependence of the NN interaction, but especially the former, are important for nuclear saturation. The required scalar and vector coupling constants agree fairly well with those obtained from analyses of NN scattering phase shifts with one-boson-exchange models. The mean field theory provides a semiquantitative justification for the weak Skyrme interaction in odd states. The strength of the required nonlinear term is roughly consistent with that derived using a new version of the chiral mean field theory in which the vector mass as well as the nucleon mass is generated by the sigma-field. (orig.)

Integrable model of Yang-Mills theory with scalar field and quasi-instantons

International Nuclear Information System (INIS)

Yatsun, V.A.

1988-01-01

In the framework of Euclidean conformally invariant Yang-Mills theory with a scalar field a study is made of a Hamiltonian system with two degrees of freedom that is integrable for a definite relationship between the coupling constants. A particular solution of the Hamilton-Jacobi equation leads to first-order equations that ensure a nonself-dual solution of instanton type of the considered model. As generalization of the first-order equations a quasiself-dual equation that can be integrated by means of the 't Hooft ansatz and leads to quasiself-dual instantons - quasi-instantons - is proposed

A generalized Tu formula and Hamiltonian structures of fractional AKNS hierarchy

International Nuclear Information System (INIS)

Wu, Guo-cheng; Zhang, Sheng

2011-01-01

In this Letter, a generalized Tu formula is firstly presented to construct Hamiltonian structures of fractional soliton equations. The obtained results can be reduced to the classical Hamiltonian hierarchy of AKNS in ordinary calculus. -- Highlights: → A generalized Tu formula is first established based on the fractional variational theory for non-differentiable functions. → Hamiltonian structures of fractional AKNS hierarchy are obtained. → The classical AKNS hierarchy is just a special case of the fractional hierarchy.

A generalized Tu formula and Hamiltonian structures of fractional AKNS hierarchy

Energy Technology Data Exchange (ETDEWEB)

Wu, Guo-cheng, E-mail: wuguocheng2002@yahoo.com.cn [Key Laboratory of Numerical Simulation of Sichuan Province, Neijiang, Sichuan 641112 (China); College of Mathematics and Information Science, Neijiang Normal University, Neijiang, Sichuan 641112 (China); Zhang, Sheng, E-mail: zhshaeng@yahoo.com.cn [School of Mathematical Sciences, Dalian University of Technology, Dalian 116024 (China)

2011-10-03

In this Letter, a generalized Tu formula is firstly presented to construct Hamiltonian structures of fractional soliton equations. The obtained results can be reduced to the classical Hamiltonian hierarchy of AKNS in ordinary calculus. -- Highlights: → A generalized Tu formula is first established based on the fractional variational theory for non-differentiable functions. → Hamiltonian structures of fractional AKNS hierarchy are obtained. → The classical AKNS hierarchy is just a special case of the fractional hierarchy.

Canonical formulation of supergravity and the quantization of the ultralocal theory of gravity

International Nuclear Information System (INIS)

Pilati, M.L.

1980-01-01

This thesis consists of two parts whose only common feature is that they are Hamiltonian field theories of geometric interest. The first part is concerned with the canonical formulation of supergravity and other geometrical, supersymmetric theories. The Hamiltonian for supergravity and the spinning membrane are computed, and the possible usefulness of the Hamiltonian formalism for finding the underlying geometry described. The second part attempts to give the quantization of the ultralocal theory of gravity. Classically the ultralocal theory corresponds to dropping g/sup 1/2//sup (3)/R from the Hamiltonian. The speed of light in this theory is zero; there is no propagation of information. It is desired to have the quantum version of this theory play the role that Fock space plays in ordinary quantum field theory, i.e., to the theory about which perturbations are made to obtain the full quantum theory of gravity. The quantum theory is begun by choosing variables consistent with the three-dimensional metric's having positive-definite spectrum. The representation of these operators is then given; it is an exponential representation. The operators script-H/sub perpendicular/ and script-H/sub i/ are constructed in this representation, the properties of script-H/sub i/ implying that the theory is coordinate invariant. It is found that script-H/sub perpendicular/ cannot be realized as a constraint in this theory in the way that one expects of a quantum theory of gravity

Derivation of Hamiltonians for accelerators

Energy Technology Data Exchange (ETDEWEB)

Symon, K.R.

1997-09-12

In this report various forms of the Hamiltonian for particle motion in an accelerator will be derived. Except where noted, the treatment will apply generally to linear and circular accelerators, storage rings, and beamlines. The generic term accelerator will be used to refer to any of these devices. The author will use the usual accelerator coordinate system, which will be introduced first, along with a list of handy formulas. He then starts from the general Hamiltonian for a particle in an electromagnetic field, using the accelerator coordinate system, with time t as independent variable. He switches to a form more convenient for most purposes using the distance s along the reference orbit as independent variable. In section 2, formulas will be derived for the vector potentials that describe the various lattice components. In sections 3, 4, and 5, special forms of the Hamiltonian will be derived for transverse horizontal and vertical motion, for longitudinal motion, and for synchrobetatron coupling of horizontal and longitudinal motions. Hamiltonians will be expanded to fourth order in the variables.

PREFACE: 6th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics

Science.gov (United States)

Fring, Andreas; Jones, Hugh; Znojil, Miloslav

2008-06-01

Attempts to understand the quantum mechanics of non-Hermitian Hamiltonian systems can be traced back to the early days, one example being Heisenberg's endeavour to formulate a consistent model involving an indefinite metric. Over the years non-Hermitian Hamiltonians whose spectra were believed to be real have appeared from time to time in the literature, for instance in the study of strong interactions at high energies via Regge models, in condensed matter physics in the context of the XXZ-spin chain, in interacting boson models in nuclear physics, in integrable quantum field theories as Toda field theories with complex coupling constants, and also very recently in a field theoretical scenario in the quantization procedure of strings on an AdS5 x S5 background. Concrete experimental realizations of these types of systems in the form of optical lattices have been proposed in 2007. In the area of mathematical physics similar non-systematic results appeared sporadically over the years. However, intensive and more systematic investigation of these types of non- Hermitian Hamiltonians with real eigenvalue spectra only began about ten years ago, when the surprising discovery was made that a large class of one-particle systems perturbed by a simple non-Hermitian potential term possesses a real energy spectrum. Since then regular international workshops devoted to this theme have taken place. This special issue is centred around the 6th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics held in July 2007 at City University London. All the contributions contain significant new results or alternatively provide a survey of the state of the art of the subject or a critical assessment of the present understanding of the topic and a discussion of open problems. Original contributions from non-participants were also invited. Meanwhile many interesting results have been obtained and consensus has been reached on various central conceptual issues in the

A current value Hamiltonian Approach for Discrete time Optimal Control Problems arising in Economic Growth

OpenAIRE

Naz, Rehana

2018-01-01

Pontrygin-type maximum principle is extended for the present value Hamiltonian systems and current value Hamiltonian systems of nonlinear difference equations for uniform time step $h$. A new method termed as a discrete time current value Hamiltonian method is established for the construction of first integrals for current value Hamiltonian systems of ordinary difference equations arising in Economic growth theory.

Homoclinic Orbits for a Class of Nonperiodic Hamiltonian Systems with Some Twisted Conditions

Directory of Open Access Journals (Sweden)

Qi Wang

2013-01-01

Full Text Available By the Maslov index theory, we will study the existence and multiplicity of homoclinic orbits for a class of asymptotically linear nonperiodic Hamiltonian systems with some twisted conditions on the Hamiltonian functions.

Hamiltonian approach to second order gauge invariant cosmological perturbations

Science.gov (United States)

Domènech, Guillem; Sasaki, Misao

2018-01-01

In view of growing interest in tensor modes and their possible detection, we clarify the definition of tensor modes up to 2nd order in perturbation theory within the Hamiltonian formalism. Like in gauge theory, in cosmology the Hamiltonian is a suitable and consistent approach to reduce the gauge degrees of freedom. In this paper we employ the Faddeev-Jackiw method of Hamiltonian reduction. An appropriate set of gauge invariant variables that describe the dynamical degrees of freedom may be obtained by suitable canonical transformations in the phase space. We derive a set of gauge invariant variables up to 2nd order in perturbation expansion and for the first time we reduce the 3rd order action without adding gauge fixing terms. In particular, we are able to show the relation between the uniform-ϕ and Newtonian slicings, and study the difference in the definition of tensor modes in these two slicings.

Hamiltonian formulation of the supermembrane

International Nuclear Information System (INIS)

Bergshoeff, E.; Sezgin, E.; Tanii, Y.

1987-06-01

The Hamiltonian formulation of the supermembrane theory in eleven dimensions is given. The covariant split of the first and second class constraints is exhibited, and their Dirac brackets are computed. Gauge conditions are imposed in such a way that the reparametrizations of the membrane with divergence free 2-vectors are unfixed. (author). 10 refs

String field theory

International Nuclear Information System (INIS)

Kaku, M.

1987-01-01

In this article, the authors summarize the rapid progress in constructing string field theory actions, such as the development of the covariant BRST theory. They also present the newer geometric formulation of string field theory, from which the BRST theory and the older light cone theory can be derived from first principles. This geometric formulation allows us to derive the complete field theory of strings from two geometric principles, in the same way that general relativity and Yang-Mills theory can be derived from two principles based on global and local symmetry. The geometric formalism therefore reduces string field theory to a problem of finding an invariant under a new local gauge group they call the universal string group (USG). Thus, string field theory is the gauge theory of the universal string group in much the same way that Yang-Mills theory is the gauge theory of SU(N). The geometric formulation places superstring theory on the same rigorous group theoretical level as general relativity and gauge theory

Classical effective Hamiltonians, Wigner functions, and the sign problem

International Nuclear Information System (INIS)

Samson, J.H.

1995-01-01

In the functional-integral technique an auxiliary field, coupled to appropriate operators such as spins, linearizes the interaction term in a quantum many-body system. The partition function is then averaged over this time-dependent stochastic field. Quantum Monte Carlo methods evaluate this integral numerically, but suffer from the sign (or phase) problem: the integrand may not be positive definite (or not real). It is shown that, in certain cases that include the many-band Hubbard model and the Heisenberg model, the sign problem is inevitable on fundamental grounds. Here, Monte Carlo simulations generate a distribution of incompatible operators---a Wigner function---from which expectation values and correlation functions are to be calculated; in general no positive-definite distribution of this form exists. The distribution of time-averaged auxiliary fields is the convolution of this operator distribution with a Gaussian of variance proportional to temperature, and is interpreted as a Boltzmann distribution exp(-βV eff ) in classical configuration space. At high temperatures and large degeneracies this classical effective Hamiltonian V eff tends to the static approximation as a classical limit. In the low-temperature limit the field distribution becomes a Wigner function, the sign problem occurs, and V eff is complex. Interpretations of the distributions, and a criterion for their positivity, are discussed. The theory is illustrated by an exact evaluation of the Wigner function for spin s and the effective classical Hamiltonian for the spin-1/2 van der Waals model. The field distribution can be negative here, more noticeably if the number of spins is odd

Exponentially Biased Ground-State Sampling of Quantum Annealing Machines with Transverse-Field Driving Hamiltonians.

Science.gov (United States)

Mandrà, Salvatore; Zhu, Zheng; Katzgraber, Helmut G

2017-02-17

We study the performance of the D-Wave 2X quantum annealing machine on systems with well-controlled ground-state degeneracy. While obtaining the ground state of a spin-glass benchmark instance represents a difficult task, the gold standard for any optimization algorithm or machine is to sample all solutions that minimize the Hamiltonian with more or less equal probability. Our results show that while naive transverse-field quantum annealing on the D-Wave 2X device can find the ground-state energy of the problems, it is not well suited in identifying all degenerate ground-state configurations associated with a particular instance. Even worse, some states are exponentially suppressed, in agreement with previous studies on toy model problems [New J. Phys. 11, 073021 (2009)NJOPFM1367-263010.1088/1367-2630/11/7/073021]. These results suggest that more complex driving Hamiltonians are needed in future quantum annealing machines to ensure a fair sampling of the ground-state manifold.

Adaptive control of port-Hamiltonian systems

NARCIS (Netherlands)

Dirksz, D.A.; Scherpen, J.M.A.; Edelmayer, András

2010-01-01

In this paper an adaptive control scheme is presented for general port-Hamiltonian systems. Adaptive control is used to compensate for control errors that are caused by unknown or uncertain parameter values of a system. The adaptive control is also combined with canonical transformation theory for

Remarks on Hamiltonian structures in G2-geometry

International Nuclear Information System (INIS)

Cho, Hyunjoo; Salur, Sema; Todd, A. J.

2013-01-01

In this article, we treat G 2 -geometry as a special case of multisymplectic geometry and make a number of remarks regarding Hamiltonian multivector fields and Hamiltonian differential forms on manifolds with an integrable G 2 -structure; in particular, we discuss existence and make a number of identifications of the spaces of Hamiltonian structures associated to the two multisymplectic structures associated to an integrable G 2 -structure. Along the way, we prove some results in multisymplectic geometry that are generalizations of results from symplectic geometry

Gravitational dynamics in s+1+1 dimensions II. Hamiltonian theory

International Nuclear Information System (INIS)

Kovacs, Zoltan; Gergely, Laszlo A.

2008-01-01

We develop a Hamiltonian formalism of braneworld gravity, which singles out two preferred, mutually orthogonal directions. One is a unit twist-free field of spatial vectors with integral lines intersecting perpendicularly the brane. The other is a temporal vector field with respect to which we perform the Arnowitt-Deser-Misner decomposition of the Einstein-Hilbert Lagrangian. The gravitational variables arise from the projections of the spatial metric and their canonically conjugated momenta as tensorial, vectorial and scalar quantities defined on the family of hypersurfaces containing the brane. They represent the gravitons, a gravi-photon, and a gravi-scalar, respectively. From the action we derive the canonical evolution equations and the constraints for these gravitational degrees of freedom both on the brane and outside it. By integrating across the brane, the dynamics also generates the tensorial and scalar projection of the Lanczos equation. The vectorial projection of the Lanczos equation arises in a similar way from the diffeomorphism constraint. Both the graviton and the gravi-scalar are continuous across the brane, however the momentum of the gravi-vector has a jump, related to the energy transport (heat flow) on the brane

String theory or field theory?

International Nuclear Information System (INIS)

Marshakov, Andrei V

2002-01-01

The status of string theory is reviewed, and major recent developments - especially those in going beyond perturbation theory in the string theory and quantum field theory frameworks - are analyzed. This analysis helps better understand the role and place of string theory in the modern picture of the physical world. Even though quantum field theory describes a wide range of experimental phenomena, it is emphasized that there are some insurmountable problems inherent in it - notably the impossibility to formulate the quantum theory of gravity on its basis - which prevent it from being a fundamental physical theory of the world of microscopic distances. It is this task, the creation of such a theory, which string theory, currently far from completion, is expected to solve. In spite of its somewhat vague current form, string theory has already led to a number of serious results and greatly contributed to progress in the understanding of quantum field theory. It is these developments which are our concern in this review. (reviews of topical problems)

A geometric Hamiltonian description of composite quantum systems and quantum entanglement

Science.gov (United States)

Pastorello, Davide

2015-05-01

Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is discussed in this paper. As summarized in the first part of this work, in the Hamiltonian formulation the phase space of a quantum system is the Kähler manifold given by the complex projective space P(H) of the Hilbert space H of the considered quantum theory. However the phase space of a bipartite system must be P(H1 ⊗ H2) and not simply P(H1) × P(H2) as suggested by the analogy with Classical Mechanics. A part of this paper is devoted to manage this problem. In the second part of the work, a definition of quantum entanglement and a proposal of entanglement measure are given in terms of a geometrical point of view (a rather studied topic in recent literature). Finally two known separability criteria are implemented in the Hamiltonian formalism.

The (confinement) structure of Yang-Mills-theories within a Bose-BCS-theory

International Nuclear Information System (INIS)

Schuette, D.

1984-01-01

It is the purpose of this talk to report on a first attempt to apply (non-perturbative) techniques of many-body theory to a field-theory of the Yang-Mills-type. The procedure is in principle analogous to lattice calculations: In order to make the field-theoretical hamiltonian a well-behaved operator in the Fock-space, a phasespace-cutoff is assumed for the definition of the field operators. The coupling constant g then becomes a function of this cutoff which is fixed by some physical property like a glue-ball mass. (orig./HSI)

Coherent states of quantum systems. [Hamiltonians, variable magnetic field, adiabatic approximation

Energy Technology Data Exchange (ETDEWEB)

Trifonov, D A

1975-01-01

Time-evolution of coherent states and uncertainty relations for quantum systems are considered as well as the relation between the various types of coherent states. The most general form of the Hamiltonians that keep the uncertainty products at a minimum is found using the coherent states. The minimum uncertainty packets are shown to be coherent states of the type nonstationary-system coherent states. Two specific systems, namely that of a generalized N-dimensional oscillator and that of a charged particle moving in a variable magnetic field, are treated as examples. The adiabatic approximation to the uncertainty products for these systems is also discussed and the minimality is found to be retained with an exponential accuracy.

Superconformal gravity in Hamiltonian form: another approach to the renormalization of gravitation

International Nuclear Information System (INIS)

Kaku, M.

1983-01-01

We reexpress superconformal gravity in Hamiltonian form, explicitly displaying all 24 generators of the group as Dirac constraints on the Hilbert space. From this, we can establish a firm foundation for the canonical quantization of superconformal gravity. The purpose of writing down the Hamiltonian form of the theory is to reexamine the question of renormalization and unitarity. Usually, we start with unitary theories of gravity, such as the Einstein-Hilbert action or supergravity, both of which are probably not renormalizable. In this series of papers, we take the opposite approach and start with a theory which is renormalizable but has problems with unitarity. Conformal and superconformal gravity are both plagued with dipole ghosts when we use perturbation theory to quantize the theories. It is difficult to interpret the results of perturbation theory because the asymptotic states have zero norm and the potential between particles grows linearly with the separation distance. The purpose of writing the Hamiltonian form of these theories is to approach the question of unitarity from a different point of view. For example, a strong-coupling approach to these theories may yield a totally different perturbation expansion. We speculate that canonically quantizing the theory by power expanding in the strong-coupling regime may yield a different set of asymptotic states, somewhat similar to the situation in gauge theories. In this series of papers, we wish to reopen the question of the unitarity of conformal theories. We conjecture that ghosts are ''confined.''

T-duality transformation and universal structure of noncritical string field theory

International Nuclear Information System (INIS)

Asatani, T.; Kuroki, T.; Okawa, Y.; Sugino, F.; Yoneya, T.

1997-01-01

We discuss a T-duality transformation for the c=1/2 matrix model for the purpose of studying duality transformations in a possible toy example of nonperturbative frameworks of string theory. Our approach is to first investigate the scaling limit of the Schwinger-Dyson equations and the stochastic Hamiltonian in terms of the dual variables and then compare the results with those using the original spin variables. It is shown that the c=1/2 model in the scaling limit is T-duality symmetric in the sphere approximation. In the case of the standard two-matrix model, however, the duality symmetry is violated when the higher-genus effects are taken into account, due to the nonsymmetrical appearence of global Z 2 vector fields corresponding to nontrivial homology cycles. Some universal properties of the stochastic Hamiltonians which play an important role in discussing the scaling limit and have been discussed in a previous work by Sugino and Yoneya are refined in both the original and dual formulations. We also report a number of new explicit results for various amplitudes containing macroscopic loop operators. copyright 1997 The American Physical Society

Two-color Fermi-liquid theory for transport through a multilevel Kondo impurity

Science.gov (United States)

Karki, D. B.; Mora, Christophe; von Delft, Jan; Kiselev, Mikhail N.

2018-05-01

We consider a quantum dot with K ≥2 orbital levels occupied by two electrons connected to two electric terminals. The generic model is given by a multilevel Anderson Hamiltonian. The weak-coupling theory at the particle-hole symmetric point is governed by a two-channel S =1 Kondo model characterized by intrinsic channels asymmetry. Based on a conformal field theory approach we derived an effective Hamiltonian at a strong-coupling fixed point. The Hamiltonian capturing the low-energy physics of a two-stage Kondo screening represents the quantum impurity by a two-color local Fermi liquid. Using nonequilibrium (Keldysh) perturbation theory around the strong-coupling fixed point we analyze the transport properties of the model at finite temperature, Zeeman magnetic field, and source-drain voltage applied across the quantum dot. We compute the Fermi-liquid transport constants and discuss different universality classes associated with emergent symmetries.

Interactions and scattering in d = 1 string theory

International Nuclear Information System (INIS)

Sengupta, A.M.; Mandal, G.; Wadia, S.R.

1991-01-01

This paper discusses two results: the authors calculate the two-point function of the density fluctuations to o(g st 2 ) in the fermionic formulation of the d = 1 string theory and compare with the o(g st 2 ) result from the candidate collective field Hamiltonian. The latter result is divergent, showing the inequivalence of the two theories. The authors find out the corrections to the collective field Hamiltonian (both in the form of infinite counterterms and additional finite pieces) needed to match with the fermion theory. The authors study tree-level scattering processes between bosons due to the localized interaction near the boundary (in a region of order √ α'). The reflection problem at the boundary is treated by an analytic continuation of the time-of-flight variable

Accurate nonadiabatic quantum dynamics on the cheap: Making the most of mean field theory with master equations

Energy Technology Data Exchange (ETDEWEB)

Kelly, Aaron; Markland, Thomas E., E-mail: tmarkland@stanford.edu [Department of Chemistry, Stanford University, Stanford, California 94305 (United States); Brackbill, Nora [Department of Physics, Stanford University, Stanford, California 94305 (United States)

2015-03-07

In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.

Accurate nonadiabatic quantum dynamics on the cheap: making the most of mean field theory with master equations.

Science.gov (United States)

Kelly, Aaron; Brackbill, Nora; Markland, Thomas E

2015-03-07

In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.

Geophysical Field Theory

International Nuclear Information System (INIS)

Eloranta, E.

2003-11-01

The geophysical field theory includes the basic principles of electromagnetism, continuum mechanics, and potential theory upon which the computational modelling of geophysical phenomena is based on. Vector analysis is the main mathematical tool in the field analyses. Electrostatics, stationary electric current, magnetostatics, and electrodynamics form a central part of electromagnetism in geophysical field theory. Potential theory concerns especially gravity, but also electrostatics and magnetostatics. Solid state mechanics and fluid mechanics are central parts in continuum mechanics. Also the theories of elastic waves and rock mechanics belong to geophysical solid state mechanics. The theories of geohydrology and mass transport form one central field theory in geophysical fluid mechanics. Also heat transfer is included in continuum mechanics. (orig.)

A Class of Quasi-exact Solutions of Rabi Hamiltonian

International Nuclear Information System (INIS)

Pan Feng; Yao Youkun; Xie Mingxia; Han Wenjuan; Draayer, J.P.

2007-01-01

A class of quasi-exact solutions of the Rabi Hamiltonian, which describes a two-level atom interacting with a single-mode radiation field via a dipole interaction without the rotating-wave approximation, are obtained by using a wavefunction ansatz. Exact solutions for part of the spectrum are obtained when the atom-field coupling strength and the field frequency satisfy certain relations. As an example, the lowest exact energy level and the corresponding atom-field entanglement at the quasi-exactly solvable point are calculated and compared to results from the Jaynes-Cummings and counter-rotating cases of the Rabi Hamiltonian.

Quantum field theory

International Nuclear Information System (INIS)

Ryder, L.H.

1985-01-01

This introduction to the ideas and techniques of quantum field theory presents the material as simply as possible and is designed for graduate research students. After a brief survey of particle physics, the quantum theory of scalar and spinor fields and then of gauge fields, is developed. The emphasis throughout is on functional methods, which have played a large part in modern field theory. The book concludes with a bridge survey of ''topological'' objects in field theory and assumes a knowledge of quantum mechanics and special relativity

Classical field theory

CERN Document Server

Franklin, Joel

2017-01-01

Classical field theory, which concerns the generation and interaction of fields, is a logical precursor to quantum field theory, and can be used to describe phenomena such as gravity and electromagnetism. Written for advanced undergraduates, and appropriate for graduate level classes, this book provides a comprehensive introduction to field theories, with a focus on their relativistic structural elements. Such structural notions enable a deeper understanding of Maxwell's equations, which lie at the heart of electromagnetism, and can also be applied to modern variants such as Chern–Simons and Born–Infeld. The structure of field theories and their physical predictions are illustrated with compelling examples, making this book perfect as a text in a dedicated field theory course, for self-study, or as a reference for those interested in classical field theory, advanced electromagnetism, or general relativity. Demonstrating a modern approach to model building, this text is also ideal for students of theoretic...

On dipole interaction of the oxcillator with a scalar field

International Nuclear Information System (INIS)

Razumov, A.V.; Taranov, A.Yu.

1979-01-01

Dipole interaction of the oscillator with scalar field in one-dimensional case is studied. Solutions of the classical equations of motion are found and the conditions of the boundedness of the classical Hamiltonian from below are obtained. In the quantum theory the problem of choosing the zeroth approximation of perturbation theory in the case when the spectra of the free and complete Hamiltonian do not coincide with each other, is analysed

NATO Advanced Study Institute on Hamiltonian Dynamical Systems and Applications

CERN Document Server

2008-01-01

Physical laws are for the most part expressed in terms of differential equations, and natural classes of these are in the form of conservation laws or of problems of the calculus of variations for an action functional. These problems can generally be posed as Hamiltonian systems, whether dynamical systems on finite dimensional phase space as in classical mechanics, or partial differential equations (PDE) which are naturally of infinitely many degrees of freedom. This volume is the collected and extended notes from the lectures on Hamiltonian dynamical systems and their applications that were given at the NATO Advanced Study Institute in Montreal in 2007. Many aspects of the modern theory of the subject were covered at this event, including low dimensional problems as well as the theory of Hamiltonian systems in infinite dimensional phase space; these are described in depth in this volume. Applications are also presented to several important areas of research, including problems in classical mechanics, continu...

Conformal blocks in Virasoro and W theories: Duality and the Calogero-Sutherland model

International Nuclear Information System (INIS)

Estienne, Benoit; Pasquier, Vincent; Santachiara, Raoul; Serban, Didina

2012-01-01

We study the properties of the conformal blocks of the conformal field theories with Virasoro or W-extended symmetry. When the conformal blocks contain only second-order degenerate fields, the conformal blocks obey second order differential equations and they can be interpreted as ground-state wave functions of a trigonometric Calogero-Sutherland Hamiltonian with non-trivial braiding properties. A generalized duality property relates the two types of second order degenerate fields. By studying this duality we found that the excited states of the Calogero-Sutherland Hamiltonian are characterized by two partitions, or in the case of WA k-1 theories by k partitions. By extending the conformal field theories under consideration by a u(1) field, we find that we can put in correspondence the states in the Hilbert state of the extended CFT with the excited non-polynomial eigenstates of the Calogero-Sutherland Hamiltonian. When the action of the Calogero-Sutherland integrals of motion is translated on the Hilbert space, they become identical to the integrals of motion recently discovered by Alba, Fateev, Litvinov and Tarnopolsky in Liouville theory in the context of the AGT conjecture. Upon bosonization, these integrals of motion can be expressed as a sum of two, or in general k, bosonic Calogero-Sutherland Hamiltonian coupled by an interaction term with a triangular structure. For special values of the coupling constant, the conformal blocks can be expressed in terms of Jack polynomials with pairing properties, and they give electron wave functions for special Fractional Quantum Hall states.

Massive Yang-Mills fields in the Kemmer's formulation

International Nuclear Information System (INIS)

Santana Cordolino, L.A. de.

1984-01-01

The Kemmer's equation, which describes the meson, is presented in the field theory formalism. Conservated, quantities are found through the Noether's identity. This formalism is used for masive Yang-Mills fields and two equations, similar to the Kemmer's equation, are obtained, although of different formates, both containing quadratic terms. In consequence two Lagrangians are defined, formally distint, for the Yang-Mills fields. The Schroedinger-like Hamiltonian is calculated for the first wave equations. This Hamiltonian presentes one spin-Yang-Mills field interaction term, PHI jk . (L.C.) [pt

Field theories with subcanonical fields

International Nuclear Information System (INIS)

Bigi, I.I.Y.

1976-01-01

The properties of quantum field theories with spinor fields of dimension less than the canonical value of 3/2 are studied. As a starting point for the application of common perturbation theory we look for the linear version of these theories. A gange-interaction is introduced and with the aid of power counting the renormalizability of the theory is shown. It follows that in the case of a spinor-field with negative dimension renormalization can only be attained if the interaction has a further symmetry. By this symmetry the theory is determined in an unequivocal way. The gange-interaction introduced in the theory leads to a spontaneous breakdown of scale invariance whereby masses are produced. At the same time the spinor-field operators can now be separated in two orthogonal sections with opposite norm. It is proposed to use the section with negative (positive) norm to describe hadrons (leptons) respectively. (orig./WL) [de

Semiclassical analysis of the weak-coupling limit of SU(2) lattice gauge theory: The subspace of constant fields

International Nuclear Information System (INIS)

Bartels, J.; Wu, T.T.

1988-01-01

This paper contains the first part of a systematic semiclassical analysis of the weak-coupling limit of lattice gauge theories, using the Hamiltonian formulation. The model consists of an N 3 cubic lattice of pure SU(2) Yang-Mills theory, and in this first part we limit ourselves to the subspace of constant field configurations. We investigate the flow of classical trajectories, with a particular emphasis on the existence and location of caustics. There the ground-state wave function is expected to peak. It is found that regions densely filled with caustics are very close to the origin, i.e., in the domain of weak field configurations. This strongly supports the expectation that caustics are essential for quantities of physical interest

Theoretical studies of spin-Hamiltonian parameters of Mo{sup 5+} ion doped in K{sub 2}SnCl{sub 6} crystal

Energy Technology Data Exchange (ETDEWEB)

Fang, Wang, E-mail: mailfangwang@163.com; Yang, Da-Xiao; Chen, Heng-Jie; Tang, Hai-Yan

2013-11-15

The spin-Hamiltonian (SH) parameters (g factors g{sub //}, g{sub ⊥} and hyperfine structure constants A{sub //}, A{sub ⊥} ) of K{sub 2}SnCl{sub 6}: Mo{sup 5+} (4d{sup 1}) crystal are theoretically studied by the use of two microscopic spin-Hamiltonian (SH) methods, the high-order perturbation theory method (PTM) and the complete diagonalization (of energy matrix) method (CDM) within the molecular orbital (MO) scheme. The contributions arising both from the crystal field and charge transfer excitations are taken into account. The investigations show that the charge transfer mechanism plays a decisive role in the understanding of the spin-Hamiltonian (SH) parameters for 4d{sup 1} ions in crystals with the strong coordinate covalence, especially for g{sub //}>g{sub ⊥} which cannot be explained in the frame work of traditional crystal field approximation (CFA). The local defect structure around Mo{sup 5+} impurity ion center is determined to be D{sub 4} {sub h} point group symmetry.

Fundamental length in quantum theories with PT-symmetric Hamiltonians

Czech Academy of Sciences Publication Activity Database

Znojil, Miloslav

2009-01-01

Roč. 80, č. 4 (2009), 045022/1-045022/20 ISSN 1550-7998 R&D Projects: GA MŠk LC06002; GA ČR GA202/07/1307 Institutional research plan: CEZ:AV0Z10480505 Keywords : non-Hermitian Hamiltonians * anharmonic-oscillators * noncommutative space Subject RIV: BE - Theoretical Physics Impact factor: 4.922, year: 2009

Microscopic approach to critical behaviour in 3He-4He mixtures (II). Thermodynamics of the effective Hamiltonian

International Nuclear Information System (INIS)

Singh, K.K.; Goswami, P.

1984-08-01

Thermodynamics of a weakly interacting fermion-boson mixture has been worked out on the basis of the effective Hamiltonian derived in an earlier paper. Tricritical point behaviour is discussed in terms of the fields (T,μ 3 ,μ 4 ). For the degenerate phase of the mixture, the theory reproduces the classical Landau expansion near a tricritical point. For the non-degenerate phase, the theory differs materially from the Landau theory; it predicts tricritical exponents in agreement with those calculated by applying renormalization group theory to phenomenological models, and a slope for the upper line larger than that of the lambda-line in the chi-T plane. (author)

Complex Hamiltonian Dynamics

CERN Document Server

Bountis, Tassos

2012-01-01

This book introduces and explores modern developments in the well established field of Hamiltonian dynamical systems. It focuses on high degree-of-freedom systems and the transitional regimes between regular and chaotic motion. The role of nonlinear normal modes is highlighted and the importance of low-dimensional tori in the resolution of the famous FPU paradox is emphasized. Novel powerful numerical methods are used to study localization phenomena and distinguish order from strongly and weakly chaotic regimes. The emerging hierarchy of complex structures in such regimes gives rise to particularly long-lived patterns and phenomena called quasi-stationary states, which are explored in particular in the concrete setting of one-dimensional Hamiltonian lattices and physical applications in condensed matter systems.  The self-contained and pedagogical approach is blended with a unique balance between mathematical rigor, physics insights and concrete applications. End of chapter exercises and (more demanding) res...

A Tulczyjew triple for classical fields

International Nuclear Information System (INIS)

Grabowska, Katarzyna

2012-01-01

The geometrical structure known as the Tulczyjew triple has proved to be very useful in describing mechanical systems, even those with singular Lagrangians or subject to constraints. Starting from basic concepts of the variational calculus, we construct the Tulczyjew triple for first-order field theory. The important feature of our approach is that we do not postulate ad hoc the ingredients of the theory, but obtain them as unavoidable consequences of the variational calculus. This picture of field theory is covariant and complete, containing not only the Lagrangian formalism and Euler–Lagrange equations but also the phase space, the phase dynamics and the Hamiltonian formalism. Since the configuration space turns out to be an affine bundle, we have to use affine geometry, in particular the notion of the affine duality. In our formulation, the two maps α and β which constitute the Tulczyjew triple are morphisms of double structures of affine-vector bundles. We also discuss the Legendre transformation, i.e. the transition between the Lagrangian and the Hamiltonian formulation of the first-order field theory. (paper)

Hamiltonian dynamics of extended objects

Science.gov (United States)

Capovilla, R.; Guven, J.; Rojas, E.

2004-12-01

We consider relativistic extended objects described by a reparametrization-invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the dynamics of such higher derivative models which is motivated by the ADM formulation of general relativity. The canonical momenta are identified by looking at boundary behaviour under small deformations of the action; the relationship between the momentum conjugate to the embedding functions and the conserved momentum density is established. The canonical Hamiltonian is constructed explicitly; the constraints on the phase space, both primary and secondary, are identified and the role they play in the theory is described. The multipliers implementing the primary constraints are identified in terms of the ADM lapse and shift variables and Hamilton's equations are shown to be consistent with the Euler Lagrange equations.

Hamiltonian dynamics of extended objects

International Nuclear Information System (INIS)

Capovilla, R; Guven, J; Rojas, E

2004-01-01

We consider relativistic extended objects described by a reparametrization-invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the dynamics of such higher derivative models which is motivated by the ADM formulation of general relativity. The canonical momenta are identified by looking at boundary behaviour under small deformations of the action; the relationship between the momentum conjugate to the embedding functions and the conserved momentum density is established. The canonical Hamiltonian is constructed explicitly; the constraints on the phase space, both primary and secondary, are identified and the role they play in the theory is described. The multipliers implementing the primary constraints are identified in terms of the ADM lapse and shift variables and Hamilton's equations are shown to be consistent with the Euler-Lagrange equations

Fermion-dyon dynamics in non-Abelian gauge theory

International Nuclear Information System (INIS)

Pant, P.C.; Pandey, V.P.; Rajput, B.S.

1999-01-01

The study of behaviour of a fermion in the field of non-Abelian dyon has been undertaken in Lagrangian and Hamiltonian formulation. Solving Dirac equation, expression for energy Eigen value has been obtained and the Hamiltonian of this system has been shown to involve spin as well as contribution of massive fields associated with these particles. By introducing suitable spinors, the Pauli equation for a dyon moving in the field of fermion has been solved in non-Abelian gauge gauge theory and it is shown that introduction of massive fields perceptibly modifies the energy Eigen value and Eigen function of bound states of the system. (author)

Hamilton-Jacobi theorems for regular reducible Hamiltonian systems on a cotangent bundle

Science.gov (United States)

Wang, Hong

2017-09-01

In this paper, some of formulations of Hamilton-Jacobi equations for Hamiltonian system and regular reduced Hamiltonian systems are given. At first, an important lemma is proved, and it is a modification for the corresponding result of Abraham and Marsden (1978), such that we can prove two types of geometric Hamilton-Jacobi theorem for a Hamiltonian system on the cotangent bundle of a configuration manifold, by using the symplectic form and dynamical vector field. Then these results are generalized to the regular reducible Hamiltonian system with symmetry and momentum map, by using the reduced symplectic form and the reduced dynamical vector field. The Hamilton-Jacobi theorems are proved and two types of Hamilton-Jacobi equations, for the regular point reduced Hamiltonian system and the regular orbit reduced Hamiltonian system, are obtained. As an application of the theoretical results, the regular point reducible Hamiltonian system on a Lie group is considered, and two types of Lie-Poisson Hamilton-Jacobi equation for the regular point reduced system are given. In particular, the Type I and Type II of Lie-Poisson Hamilton-Jacobi equations for the regular point reduced rigid body and heavy top systems are shown, respectively.

Hamiltonian partial differential equations and applications

CERN Document Server

Nicholls, David; Sulem, Catherine

2015-01-01

This book is a unique selection of work by world-class experts exploring the latest developments in Hamiltonian partial differential equations and their applications. Topics covered within are representative of the field’s wide scope, including KAM and normal form theories, perturbation and variational methods, integrable systems, stability of nonlinear solutions as well as applications to cosmology, fluid mechanics and water waves. The volume contains both surveys and original research papers and gives a concise overview of the above topics, with results ranging from mathematical modeling to rigorous analysis and numerical simulation. It will be of particular interest to graduate students as well as researchers in mathematics and physics, who wish to learn more about the powerful and elegant analytical techniques for Hamiltonian partial differential equations.

Field theory methods applied for the study of superconductivity in one-dimensional systems; Metodos de teoria de campos no estudo da supercondutividade em sistemas unidimensionais

Energy Technology Data Exchange (ETDEWEB)

Martins, M J

1987-12-31

It is shown that the Froehlich`s hamiltonian in one spatial dimension is identical to that of an exactly solvable field Theory. The spectrum of the theory is computed. A critical coupling is found above which the system becomes unstable, indicating a superconducting transition. It is also proposed and investigated a renormalizable relativistic field theory model in two space-time dimensions, with quartic self-interaction among N species of fermions, which undergoes dynamical generation of a superconducting gap and is asymptotically free. A finite temperature is introduced and, for N -> {infinity} a critical value T{sub c} is found above which the gap vanishes. (author).

Transverse Lattice Approach to Light-Front Hamiltonian QCD

CERN Document Server

Dalley, S

1999-01-01

We describe a non-perturbative procedure for solving from first principles the light-front Hamiltonian problem of SU(N) pure gauge theory in D spacetime dimensions (D>2), based on enforcing Lorentz covariance of observables. A transverse lattice regulator and colour-dielectric link fields are employed, together with an associated effective potential. We argue that the light-front vacuum is necessarily trivial for large enough lattice spacing, and clarify why this leads to an Eguchi-Kawai dimensional reduction of observables to 1+1-dimensions in the infinite N limit. The procedure is then tested by explicit calculations for 2+1-dimensional SU(infinity) gauge theory, within a first approximation to the lattice effective potential. We identify a scaling trajectory which produces Lorentz covariant behaviour for the lightest glueballs. The predicted masses, in units of the measured string tension, are in agreement with recent results from conventional Euclidean lattice simulations. In addition, we obtain the poten...

String theory or field theory?

International Nuclear Information System (INIS)

Marshakov, A.V.

2002-01-01

The status of string theory is reviewed, and major recent developments - especially those in going beyond perturbation theory in the string theory and quantum field theory frameworks - are analyzed. This analysis helps better understand the role and place of experimental phenomena, it is emphasized that there are some insurmountable problems inherent in it - notably the impossibility to formulate the quantum theory of gravity on its basis - which prevent it from being a fundamental physical theory of the world of microscopic distances. It is this task, the creation of such a theory, which string theory, currently far from completion, is expected to solve. In spite of its somewhat vague current form, string theory has already led to a number of serious results and greatly contributed to progress in the understanding of quantum field theory. It is these developments, which are our concern in this review [ru

BPS limit of multi- D- and DF-strings in boundary string field theory

International Nuclear Information System (INIS)

Go, Gyungchoon; Ishida, Akira; Kim, Yoonbai

2007-01-01

A BPS limit is systematically derived for straight multi- D- and DF-strings from the D3D-bar3 system in the context of boundary superstring field theory. The BPS limit is obtained in the limit of thin D(F)-strings, where the Bogomolny equation supports singular static multi-D(F)-string solutions. For the BPS multi-string configurations with arbitrary separations, BPS sum rule is fulfilled under a Gaussian type tachyon potential and reproduces exactly the descent relation. For the DF-strings ((p,q)-strings), the distribution of fundamental string charge density coincides with its energy density and the Hamiltonian density takes the BPS formula of square-root form

The bi-Hamiltonian structures of the Manin-Radul super KP hierarchy

International Nuclear Information System (INIS)

Panda, S.; Roy, S.

1992-05-01

We consider the ''even-time'' flow of the Manin-Radul supersymmetric KP hierarchy and show that it possesses bi-Hamiltonian structures by deriving two distinct Gelfand-Dikii brackets corresponding to two successive Hamiltonians of the system. A recursion relation involving them is also obtained. We observe that the first Hamiltonian structure defines a supersymmetric Lie algebra since it is a linear algebra among the super fields appearing in the Lax operator whereas the second Hamiltonian structure is a non-linear algebra and so it does not define a Lie algebra. (author). 25 refs

Steiner systems and large non-Hamiltonian hypergraphs

Directory of Open Access Journals (Sweden)

Zsolt Tuza

2006-10-01

Full Text Available From Steiner systems S(k − 2, 2k − 3, v, we construct k-uniform hyper- graphs of large size without Hamiltonian cycles. This improves previous estimates due to G. Y. Katona and H. Kierstead [J. Graph Theory 30 (1999, pp.  205–212].

Analytic calculations of masses in Hamiltonian lattice theories

International Nuclear Information System (INIS)

Horn, D.

1985-01-01

The t-expansion of the vacuum energy function is discussed and several relations involving the connected matrix elements of powers of the hamiltonian are established. On the basis of these relations we show that the masses of the lowest lying O ++ states can be expressed as ratios of derivatives of the energy function. Other sectors of Hilbert space are discussed and a recent result for the SU(2) glueball mass, derived by using such relations as described here, is briefly reviewed. (author)

Reductions of topologically massive gravity I: Hamiltonian analysis of second order degenerate Lagrangians

Science.gov (United States)

Ćaǧatay Uçgun, Filiz; Esen, Oǧul; Gümral, Hasan

2018-01-01

We present Skinner-Rusk and Hamiltonian formalisms of second order degenerate Clément and Sarıoğlu-Tekin Lagrangians. The Dirac-Bergmann constraint algorithm is employed to obtain Hamiltonian realizations of Lagrangian theories. The Gotay-Nester-Hinds algorithm is used to investigate Skinner-Rusk formalisms of these systems.

Hamiltonian reduction and supersymmetric mechanics with Dirac monopole

International Nuclear Information System (INIS)

Bellucci, Stefano; Nersessian, Armen; Yeranyan, Armen

2006-01-01

We apply the technique of Hamiltonian reduction for the construction of three-dimensional N=4 supersymmetric mechanics specified by the presence of a Dirac monopole. For this purpose we take the conventional N=4 supersymmetric mechanics on the four-dimensional conformally-flat spaces and perform its Hamiltonian reduction to three-dimensional system. We formulate the final system in the canonical coordinates, and present, in these terms, the explicit expressions of the Hamiltonian and supercharges. We show that, besides a magnetic monopole field, the resulting system is specified by the presence of a spin-orbit coupling term. A comparision with previous work is also carried out

Unified field theory

International Nuclear Information System (INIS)

Prasad, R.

1975-01-01

Results of researches into Unified Field Theory over the past seven years are presented. The subject is dealt with in chapters entitled: the choice of affine connection, algebraic properties of the vector fields, field laws obtained from the affine connection based on the path integral method, application to quantum theory and cosmology, interpretation of physical theory in terms of geometry. (U.K.)

Finite discrete field theory

International Nuclear Information System (INIS)

Souza, Manoelito M. de

1997-01-01

We discuss the physical meaning and the geometric interpretation of implementation in classical field theories. The origin of infinities and other inconsistencies in field theories is traced to fields defined with support on the light cone; a finite and consistent field theory requires a light-cone generator as the field support. Then, we introduce a classical field theory with support on the light cone generators. It results on a description of discrete (point-like) interactions in terms of localized particle-like fields. We find the propagators of these particle-like fields and discuss their physical meaning, properties and consequences. They are conformally invariant, singularity-free, and describing a manifestly covariant (1 + 1)-dimensional dynamics in a (3 = 1) spacetime. Remarkably this conformal symmetry remains even for the propagation of a massive field in four spacetime dimensions. We apply this formalism to Classical electrodynamics and to the General Relativity Theory. The standard formalism with its distributed fields is retrieved in terms of spacetime average of the discrete field. Singularities are the by-products of the averaging process. This new formalism enlighten the meaning and the problem of field theory, and may allow a softer transition to a quantum theory. (author)

Unbounded dynamics and compact invariant sets of one Hamiltonian system defined by the minimally coupled field

Energy Technology Data Exchange (ETDEWEB)

Starkov, Konstantin E., E-mail: kstarkov@ipn.mx

2015-06-12

In this paper we study some features of global dynamics for one Hamiltonian system arisen in cosmology which is formed by the minimally coupled field; this system was introduced by Maciejewski et al. in 2007. We establish that under some simple conditions imposed on parameters of this system all trajectories are unbounded in both of time directions. Further, we present other conditions for system parameters under which we localize the domain with unbounded dynamics; this domain is defined with help of bounds for values of the Hamiltonian level surface parameter. We describe the case when our system possesses periodic orbits which are found explicitly. In the rest of the cases we get some localization bounds for compact invariant sets. - Highlights: • Domain with unbounded dynamics is localized. • Equations for periodic orbits are given in one level set. • Localizations for compact invariant sets are got.

Effective field theories

International Nuclear Information System (INIS)

Mack, G.; Kalkreuter, T.; Palma, G.; Speh, M.

1992-05-01

Effective field theories encode the predictions of a quantum field theory at low energy. The effective theory has a fairly low utraviolet cutoff. As a result, loop corrections are small, at least if the effective action contains a term which is quadratic in the fields, and physical predictions can be read straight from the effective Lagrangean. Methods will be discussed how to compute an effective low energy action from a given fundamental action, either analytically or numerically, or by a combination of both methods. Basically, the idea is to integrate out the high frequency components of fields. This requires the choice of a 'blockspin', i.e. the specification af a low frequency field as a function of the fundamental fields. These blockspins will be fields of the effective field theory. The blockspin need not be a field of the same type as one of the fundamental fields, and it may be composite. Special features of blockspin in nonabelian gauge theories will be discussed in some detail. In analytical work and in multigrid updating schemes one needs interpolation kernels A from coarse to fine grid in addition to the averaging kernels C which determines the blockspin. A neural net strategy for finding optimal kernels is presented. Numerical methods are applicable to obtain actions of effective theories on lattices of finite volume. The special case of a 'lattice' with a single site (the constraint effective potential) is of particular interest. In a higgs model, the effective action reduces in this case to the free energy, considered as a function of a gauge covariant magnetization. Its shape determines the phase structure of the theory. Its loop expansion with and without gauge fields can be used to determine finite size corrections to numerical data. (orig.)

Bjorken-Johnson-Low analysis of commutator anomalies, current-divergence anomalies, and Fujikawa's relation in chiral gauge theories

International Nuclear Information System (INIS)

Seo, K.

1990-01-01

Fermion one-loop corrections to the commutators of the gauge field, the electric field, and the charge density with the total Hamiltonian are evaluated by the Bjorken-Johnson-Low method in chiral gauge theories. It turns out that individual terms of the Hamiltonian give anomalous terms to the commutator with the electric field, but the total Hamiltonian does not. That is, the classical equation of motion for the electric field holds as the Heisenberg equation. The current-divergence anomaly is identified with the anomalous terms of the commutator between the charge density and the total Hamiltonian. These two results are combined to show that the time derivative of the Gauss-law operator amounts to the current-divergence anomaly (Fujikawa's relation)

Effective Hamiltonians for phosphorene and silicene

International Nuclear Information System (INIS)

Lew Yan Voon, L C; Lopez-Bezanilla, A; Wang, J; Zhang, Y; Willatzen, M

2015-01-01

We derived the effective Hamiltonians for silicene and phosphorene with strain, electric field and magnetic field using the method of invariants. Our paper extends the work of Geissler et al 2013 (New J. Phys. 15 085030) on silicene, and Li and Appelbaum 2014 (Phys. Rev. B 90, 115439) on phosphorene. Our Hamiltonians are compared to an equivalent one for graphene. For silicene, the expression for band warping is obtained analytically and found to be of different order than for graphene. We prove that a uniaxial strain does not open a gap, resolving contradictory numerical results in the literature. For phosphorene, it is shown that the bands near the Brillouin zone center only have terms in even powers of the wave vector. We predict that the energies change quadratically in the presence of a perpendicular external electric field but linearly in a perpendicular magnetic field, as opposed to those for silicene which vary linearly in both cases. Preliminary ab initio calculations for the intrinsic band structures have been carried out in order to evaluate some of the k⋅p parameters. (paper)

Skyrme's interaction beyond the mean-field. The DGCM+GOA Hamiltonian of nuclear quadrupole motion

International Nuclear Information System (INIS)

Kluepfel, Peter

2008-01-01

This work focuses on the microscopic description of nuclear collective quadrupole motion within the framework of the dynamic Generator-Coordinate-Method(DGCM)+Gaussian-Overlap-Approximation(GOA). Skyrme-type effective interactions are used as the fundamental many-particle interaction. Starting from a rotational invariant, polynomial and topologic consistent formulation of the GCM+GOA Hamiltonian an interpolation scheme for the collective masses and potential is developed. It allows to define the collective Hamiltonian of fully triaxial collective quadrupole dynamics from a purely axial symmetric configuration space. The substantial gain in performance allows the self-consistent evaluation of the dynamic quadrupole mass within the ATDHF-cranking model. This work presents the first large-scale analysis of quadrupole correlation energies and lowlying collective states within the DGCM+GOA model. Different Skyrme- and pairing interactions are compared from old standards up to more recent parameterizations. After checking the validity of several approximations to the DGCM+GOA model - both on the mean-field and the collective level - we proceed with a detailed investigation of correlation effects along the chains of semi-magic isotopes and isotones. This finally allows to define a set of observables which are hardly affected by collective correlations. Those observables were used for a refit of a Skyrme-type effective interaction which is expected to cure most of the problems of the recent parameterizations. Preparing further work, estimates for the correlated ground state energy are proposed which can be evaluated directly from the mean-field model. (orig.)

Skyrme's interaction beyond the mean-field. The DGCM+GOA Hamiltonian of nuclear quadrupole motion

Energy Technology Data Exchange (ETDEWEB)

Kluepfel, Peter

2008-07-29

This work focuses on the microscopic description of nuclear collective quadrupole motion within the framework of the dynamic Generator-Coordinate-Method(DGCM)+Gaussian-Overlap-Approximation(GOA). Skyrme-type effective interactions are used as the fundamental many-particle interaction. Starting from a rotational invariant, polynomial and topologic consistent formulation of the GCM+GOA Hamiltonian an interpolation scheme for the collective masses and potential is developed. It allows to define the collective Hamiltonian of fully triaxial collective quadrupole dynamics from a purely axial symmetric configuration space. The substantial gain in performance allows the self-consistent evaluation of the dynamic quadrupole mass within the ATDHF-cranking model. This work presents the first large-scale analysis of quadrupole correlation energies and lowlying collective states within the DGCM+GOA model. Different Skyrme- and pairing interactions are compared from old standards up to more recent parameterizations. After checking the validity of several approximations to the DGCM+GOA model - both on the mean-field and the collective level - we proceed with a detailed investigation of correlation effects along the chains of semi-magic isotopes and isotones. This finally allows to define a set of observables which are hardly affected by collective correlations. Those observables were used for a refit of a Skyrme-type effective interaction which is expected to cure most of the problems of the recent parameterizations. Preparing further work, estimates for the correlated ground state energy are proposed which can be evaluated directly from the mean-field model. (orig.)

Action-minimizing methods in Hamiltonian dynamics

CERN Document Server

Sorrentino, Alfonso

2015-01-01

John Mather's seminal works in Hamiltonian dynamics represent some of the most important contributions to our understanding of the complex balance between stable and unstable motions in classical mechanics. His novel approach-known as Aubry-Mather theory-singles out the existence of special orbits and invariant measures of the system, which possess a very rich dynamical and geometric structure. In particular, the associated invariant sets play a leading role in determining the global dynamics of the system. This book provides a comprehensive introduction to Mather's theory, and can serve as a

RG-Whitham dynamics and complex Hamiltonian systems

Directory of Open Access Journals (Sweden)

A. Gorsky

2015-06-01

Full Text Available Inspired by the Seiberg–Witten exact solution, we consider some aspects of the Hamiltonian dynamics with the complexified phase space focusing at the renormalization group (RG-like Whitham behavior. We show that at the Argyres–Douglas (AD point the number of degrees of freedom in Hamiltonian system effectively reduces and argue that anomalous dimensions at AD point coincide with the Berry indexes in classical mechanics. In the framework of Whitham dynamics AD point turns out to be a fixed point. We demonstrate that recently discovered Dunne–Ünsal relation in quantum mechanics relevant for the exact quantization condition exactly coincides with the Whitham equation of motion in the Ω-deformed theory.

Effective quantum field theories

International Nuclear Information System (INIS)

Georgi, H.M.

1993-01-01

The most appropriate description of particle interactions in the language of quantum field theory depends on the energy at which the interactions are studied; the description is in terms of an ''effective field theory'' that contains explicit reference only to those particles that are actually important at the energy being studied. The various themes of the article are: local quantum field theory, quantum electrodynamics, new physics, dimensional parameters and renormalizability, socio-dynamics of particle theory, spontaneously broken gauge theories, scale dependence, grand unified and effective field theories. 2 figs

Hamiltonian dynamics of extended objects

Energy Technology Data Exchange (ETDEWEB)

Capovilla, R [Departamento de FIsica, Centro de Investigacion y de Estudios Avanzados del IPN, Apdo Postal 14-740, 07000 Mexico, DF (Mexico); Guven, J [School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4 (Ireland); Rojas, E [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apdo Postal 70-543, 04510 Mexico, DF (Mexico)

2004-12-07

We consider relativistic extended objects described by a reparametrization-invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the dynamics of such higher derivative models which is motivated by the ADM formulation of general relativity. The canonical momenta are identified by looking at boundary behaviour under small deformations of the action; the relationship between the momentum conjugate to the embedding functions and the conserved momentum density is established. The canonical Hamiltonian is constructed explicitly; the constraints on the phase space, both primary and secondary, are identified and the role they play in the theory is described. The multipliers implementing the primary constraints are identified in terms of the ADM lapse and shift variables and Hamilton's equations are shown to be consistent with the Euler-Lagrange equations.

Cluster expansion for ground states of local Hamiltonians

Directory of Open Access Journals (Sweden)

Alvise Bastianello

2016-08-01

Full Text Available A central problem in many-body quantum physics is the determination of the ground state of a thermodynamically large physical system. We construct a cluster expansion for ground states of local Hamiltonians, which naturally incorporates physical requirements inherited by locality as conditions on its cluster amplitudes. Applying a diagrammatic technique we derive the relation of these amplitudes to thermodynamic quantities and local observables. Moreover we derive a set of functional equations that determine the cluster amplitudes for a general Hamiltonian, verify the consistency with perturbation theory and discuss non-perturbative approaches. Lastly we verify the persistence of locality features of the cluster expansion under unitary evolution with a local Hamiltonian and provide applications to out-of-equilibrium problems: a simplified proof of equilibration to the GGE and a cumulant expansion for the statistics of work, for an interacting-to-free quantum quench.

Field theory

CERN Multimedia

1999-11-08

In these lectures I will build up the concept of field theory using the language of Feynman diagrams. As a starting point, field theory in zero spacetime dimensions is used as a vehicle to develop all the necessary techniques: path integral, Feynman diagrams, Schwinger-Dyson equations, asymptotic series, effective action, renormalization etc. The theory is then extended to more dimensions, with emphasis on the combinatorial aspects of the diagrams rather than their particular mathematical structure. The concept of unitarity is used to, finally, arrive at the various Feynman rules in an actual, four-dimensional theory. The concept of gauge-invariance is developed, and the structure of a non-abelian gauge theory is discussed, again on the level of Feynman diagrams and Feynman rules.

Optimal control methods for rapidly time-varying Hamiltonians

International Nuclear Information System (INIS)

Motzoi, F.; Merkel, S. T.; Wilhelm, F. K.; Gambetta, J. M.

2011-01-01

In this article, we develop a numerical method to find optimal control pulses that accounts for the separation of timescales between the variation of the input control fields and the applied Hamiltonian. In traditional numerical optimization methods, these timescales are treated as being the same. While this approximation has had much success, in applications where the input controls are filtered substantially or mixed with a fast carrier, the resulting optimized pulses have little relation to the applied physical fields. Our technique remains numerically efficient in that the dimension of our search space is only dependent on the variation of the input control fields, while our simulation of the quantum evolution is accurate on the timescale of the fast variation in the applied Hamiltonian.

Adiabatic Hamiltonian deformation, linear response theory, and nonequilibrium molecular dynamics

International Nuclear Information System (INIS)

Hoover, W.G.

1980-01-01

Although Hamiltonians of various kinds have previously been used to derive Green-Kubo relations for the transport coefficients, the particular choice described is uniquely related to thermodynamics. This nonequilibrium Hamiltonian formulation of fluid flow provides pedagogically simple routes to nonequilibrium fluxes and distribution functions, to theoretical understanding of long-time effects, and to new numerical methods for simulating systems far from equilibrium. The same methods are now being applied to solid-phase problems. At the relatively high frequencies used in the viscous fluid calculations described, solids typically behave elastically. Lower frequencies lead to the formation of dislocations and other defects, making it possible to study plastic flow. A property of the nonequilibrium equations of motion which might be profitably explored is their effective irreversibility. Because only a few particles are necessary to generate irreversible behavior, simulations using adiabatic deformations of the kind described here could perhaps elucidate the instability in the equations of motion responsible for irreversibility

Dirac equation in magnetic-solenoid field

Energy Technology Data Exchange (ETDEWEB)

Gavrilov, S.P. [Dept. Fisica e Quimica, UNESP, Campus de Guaratingueta (Brazil); Gitman, D.M.; Smirnov, A.A. [Instituto de Fisica, Universidade de Sao Paulo (Brazil)

2004-07-01

We consider the Dirac equation in the magnetic-solenoid field (the field of a solenoid and a collinear uniform magnetic field). For the case of Aharonov-Bohm solenoid, we construct self-adjoint extensions of the Dirac Hamiltonian using von Neumann's theory of deficiency indices. We find self-adjoint extensions of the Dirac Hamiltonian and boundary conditions at the AB solenoid. Besides, for the first time, solutions of the Dirac equation in the magnetic-solenoid field with a finite radius solenoid were found. We study the structure of these solutions and their dependence on the behavior of the magnetic field inside the solenoid. Then we exploit the latter solutions to specify boundary conditions for the magnetic-solenoid field with Aharonov-Bohm solenoid. (orig.)

Field theory and strings

International Nuclear Information System (INIS)

Bonara, L.; Cotta-Ramusino, P.; Rinaldi, M.

1987-01-01

It is well-known that type I and heterotic superstring theories have a zero mass spectrum which correspond to the field content of N=1 supergravity theory coupled to supersymmetric Yang-Mills theory in 10-D. The authors study the field theory ''per se'', in the hope that simple consistency requirements will determine the theory completely once one knows the field content inherited from string theory. The simplest consistency requirements are: N=1 supersymmetry; and absence of chiral anomalies. This is what the authors discuss in this paper here leaving undetermined the question of the range of validity of the resulting field theory. As is known, a model of N=1 supergravity (SUGRA) coupled to supersymmetric Yang-Mills (SYM) theory was known in the form given by Chapline and Manton. The coupling of SUGRA to SYM was determined by the definition of the ''field strength'' 3-form H in this paper

The geometric approach to sets of ordinary differential equations and Hamiltonian dynamics

Science.gov (United States)

Estabrook, F. B.; Wahlquist, H. D.

1975-01-01

The calculus of differential forms is used to discuss the local integration theory of a general set of autonomous first order ordinary differential equations. Geometrically, such a set is a vector field V in the space of dependent variables. Integration consists of seeking associated geometric structures invariant along V: scalar fields, forms, vectors, and integrals over subspaces. It is shown that to any field V can be associated a Hamiltonian structure of forms if, when dealing with an odd number of dependent variables, an arbitrary equation of constraint is also added. Families of integral invariants are an immediate consequence. Poisson brackets are isomorphic to Lie products of associated CT-generating vector fields. Hamilton's variational principle follows from the fact that the maximal regular integral manifolds of a closed set of forms must include the characteristics of the set.

Relative volume of Kolmogorov–Arnold–Moser tori and uniform distribution, stickiness and nonstickiness in Hamiltonian systems

International Nuclear Information System (INIS)

Bunimovich, Leonid A

2008-01-01

We discuss several open problems in the theory of Hamiltonian systems. They are all related to the Hamiltonian systems with divided phase space, where Kolmogorov–Arnold–Moser tori coexist with ergodic components of positive measure. (open problem)

Contact Hamiltonian mechanics

Energy Technology Data Exchange (ETDEWEB)

Bravetti, Alessandro, E-mail: alessandro.bravetti@iimas.unam.mx [Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, A. P. 70543, México, DF 04510 (Mexico); Cruz, Hans, E-mail: hans@ciencias.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A. P. 70543, México, DF 04510 (Mexico); Tapias, Diego, E-mail: diego.tapias@nucleares.unam.mx [Facultad de Ciencias, Universidad Nacional Autónoma de México, A.P. 70543, México, DF 04510 (Mexico)

2017-01-15

In this work we introduce contact Hamiltonian mechanics, an extension of symplectic Hamiltonian mechanics, and show that it is a natural candidate for a geometric description of non-dissipative and dissipative systems. For this purpose we review in detail the major features of standard symplectic Hamiltonian dynamics and show that all of them can be generalized to the contact case.

The 4-particle hydrogen-anti-hydrogen system revisited. Twofold molecular Hamiltonian symmetry and natural atom anti-hydrogen

International Nuclear Information System (INIS)

Van Hooydonk, G.

2005-01-01

The historical importance of the original quantum mechanical bond theory proposed by Heitler and London in 1927 as well as its pitfalls are reviewed. Modern ab initio treatments of H-H-bar systems are inconsistent with the logic behind algebraic Hamiltonians H ± = H 0 ± ΔH for charge-symmetrical and charge-asymmetrical 4 unit charge systems like H 2 and HH-bar. Their eigenvalues are exactly those of 1927 Heitler-London (HL) theory. Since these 2 Hamiltonians are mutually exclusive, only the attractive one can apply for stable natural molecular H 2 . A wrong choice leads to problems with anti-atom H-bar. In line with earlier results on band and line spectra, we now prove that HL chose the wrong Hamiltonian for H 2 . Their theory explains the stability of attractive system H 2 with a repulsive Hamiltonian H 0 + ΔH instead of with the attractive one H 0 - ΔH, representative for charge-asymmetrical system HH-bar. A new second order symmetry effect is detected in this attractive Hamiltonian, which leads to a 3-dimensional structure for the 4-particle system. Repulsive HL Hamiltonian H + applies at long range but at the critical distance, attractive charge-inverted Hamiltonian H - takes over and leads to bond H 2 but in reality, HH-bar, for which we give an analytical proof. This analysis confirms and generalizes an earlier critique of the wrong long range behavior of HL-theory by Bingel, Preuss and Schmidtke and by Herring. Another wrong asymptote choice in the past also applies for atomic anti-hydrogen H-bar, which has hidden the Mexican hat potential for natural hydrogen. This generic solution removes most problems, physicists and chemists experience with atomic H-bar and molecular HH-bar, including the problem with antimatter in the Universe. (author)

Noncanonical Hamiltonian methods in plasma dynamics

International Nuclear Information System (INIS)

Kaufman, A.N.

1982-01-01

A Hamiltonian approach to plasma dynamics is described. The Poisson bracket of two observables g 1 and g 2 is given by using an antisymmetric tensor J, and must satisfy the Jacobi condition. The J can be obtained by elementary tensor analysis. The evolution in time of an observable g is given in terms of the Poisson bracket and a Hamiltonian H(Z). The guiding-center description of particle motion was presented by Littlejohn. The ponderomotive drift and force, the wave-induced oscillation-center velocity, and the gyrofrequency shift are obtained. The Lie transform yields the wave-induced increment to the gyromomentum. In the coulomb model for a Vlasov system, the dynamical variable is the Vlasov distribution f(z). The Hamiltonian functional and the Poisson bracket are obtained. The coupling of f(z) to the Maxwell field appears in the Poisson bracket. The evolution equation yields the Vlasov-Maxwell system. (Kato, T.)

Algebraic conformal field theory

International Nuclear Information System (INIS)

Fuchs, J.; Nationaal Inst. voor Kernfysica en Hoge-Energiefysica

1991-11-01

Many conformal field theory features are special versions of structures which are present in arbitrary 2-dimensional quantum field theories. So it makes sense to describe 2-dimensional conformal field theories in context of algebraic theory of superselection sectors. While most of the results of the algebraic theory are rather abstract, conformal field theories offer the possibility to work out many formulae explicitly. In particular, one can construct the full algebra A-bar of global observables and the endomorphisms of A-bar which represent the superselection sectors. Some explicit results are presented for the level 1 so(N) WZW theories; the algebra A-bar is found to be the enveloping algebra of a Lie algebra L-bar which is an extension of the chiral symmetry algebra of the WZW theory. (author). 21 refs., 6 figs

Fock-space diagonalization of the state-dependent pairing Hamiltonian with the Woods-Saxon mean field

International Nuclear Information System (INIS)

Molique, H.; Dudek, J.

1997-01-01

A particle-number conserving approach is presented to solve the nuclear mean-field plus pairing Hamiltonian problem with a realistic deformed Woods-Saxon single-particle potential. The method is designed for the state-dependent monopole pairing Hamiltonian H pair =summation αβ G αβ c α † c bar α † c bar β c β with an arbitrary set of matrix elements G αβ . Symmetries of the Hamiltonians on the many-body level are discussed using the language of P symmetry introduced earlier in the literature and are employed to diagonalize the problem; the only essential approximation used is a many-body (Fock-space) basis cutoff. An optimal basis construction is discussed and the stability of the final result with respect to the basis cutoff is illustrated in details. Extensions of the concept of P symmetry are introduced and their consequences for an optimal many-body basis cutoff construction are exploited. An algorithm is constructed allowing to solve the pairing problems in the many-body spaces corresponding to p∼40 particles on n∼80 levels and for several dozens of lowest lying states with precision ∼(1 endash 2) % within seconds of the CPU time on a CRAY computer. Among applications, the presence of the low-lying seniority s=0 solutions, that are usually poorly described in terms of the standard approximations (BCS, HFB), is discussed and demonstrated to play a role in the interpretation of the spectra of rotating nuclei. copyright 1997 The American Physical Society

Goldstone's theorem and Hamiltonian of multi-Galileon modified gravity

International Nuclear Information System (INIS)

Zhou Shuangyong

2011-01-01

The Galileon model was recently proposed to locally describe a class of modified gravity theories, including the braneworld Dvali-Gabadadze-Porrati model. We discuss spontaneous symmetry breaking of the self-accelerating branch in a multi-Galileon theory with internal global symmetries. We show that a modified version of Goldstone's theorem is applicable to the symmetry breaking pattern and discuss its implications. We also derive the Hamiltonian of a general multi-Galileon theory and discuss its implications.

Asymptotic Conservation Laws in Classical Field Theory

International Nuclear Information System (INIS)

Anderson, I.M.; Torre, C.G.

1996-01-01

A new, general, field theoretic approach to the derivation of asymptotic conservation laws is presented. In this approach asymptotic conservation laws are constructed directly from the field equations according to a universal prescription which does not rely upon the existence of Noether identities or any Lagrangian or Hamiltonian formalisms. The resulting general expressions of the conservation laws enjoy important invariance properties and synthesize all known asymptotic conservation laws, such as the Arnowitt-Deser-Misner energy in general relativity. copyright 1996 The American Physical Society

Hamiltonian Dynamics of Doubly-Foliable Space-Times

Directory of Open Access Journals (Sweden)

Cecília Gergely

2018-01-01

Full Text Available The 2 + 1 + 1 decomposition of space-time is useful in monitoring the temporal evolution of gravitational perturbations/waves in space-times with a spatial direction singled-out by symmetries. Such an approach based on a perpendicular double foliation has been employed in the framework of dark matter and dark energy-motivated scalar-tensor gravitational theories for the discussion of the odd sector perturbations of spherically-symmetric gravity. For the even sector, however, the perpendicularity has to be suppressed in order to allow for suitable gauge freedom, recovering the 10th metric variable. The 2 + 1 + 1 decomposition of the Einstein–Hilbert action leads to the identification of the canonical pairs, the Hamiltonian and momentum constraints. Hamiltonian dynamics is then derived via Poisson brackets.

Hamiltonian theories quantization based on a probability operator

International Nuclear Information System (INIS)

Entral'go, E.E.

1986-01-01

The quantization method with a linear reflection of classical coordinate-momentum-time functions Λ(q,p,t) at quantum operators in a space of quantum states ψ, is considered. The probability operator satisfies a system of equations representing the principles of dynamical and canonical correspondences between the classical and quantum theories. The quantization based on a probability operator leads to a quantum theory with a nonnegative joint coordinate-momentum distribution function for any state ψ. The main consequences of quantum mechanics with a probability operator are discussed in comparison with the generally accepted quantum and classical theories. It is shown that a probability operator leads to an appearance of some new notions called ''subquantum'' ones. Hence the quantum theory with a probability operator does not pretend to any complete description of physical reality in terms of classical variables and by this reason contains no problems like Einstein-Podolsky-Rosen paradox. The results of some concrete problems are given: a free particle, a harmonic oscillator, an electron in the Coulomb field. These results give hope on the possibility of an experimental verification of the quantization based on a probability operator

Towards Sub-Microarsecond Rigid Earth Nutation Series in the Hamiltonian Theory

National Research Council Canada - National Science Library

Souchay, Jean; Folgueira, M

2000-01-01

...) are based on the works of Kinoshita (1977) and Wahr (1979). In Kinoshita's work, the rigid Earth nutation series were calculated by the application of the Hamiltonian canonical equations to the rotation of the rigid and elliptical Earth...

Focal points and principal solutions of linear Hamiltonian systems revisited

Science.gov (United States)

Šepitka, Peter; Šimon Hilscher, Roman

2018-05-01

In this paper we present a novel view on the principal (and antiprincipal) solutions of linear Hamiltonian systems, as well as on the focal points of their conjoined bases. We present a new and unified theory of principal (and antiprincipal) solutions at a finite point and at infinity, and apply it to obtain new representation of the multiplicities of right and left proper focal points of conjoined bases. We show that these multiplicities can be characterized by the abnormality of the system in a neighborhood of the given point and by the rank of the associated T-matrix from the theory of principal (and antiprincipal) solutions. We also derive some additional important results concerning the representation of T-matrices and associated normalized conjoined bases. The results in this paper are new even for completely controllable linear Hamiltonian systems. We also discuss other potential applications of our main results, in particular in the singular Sturmian theory.

Microcanonical quantum field theory

International Nuclear Information System (INIS)

Strominger, A.

1983-01-01

Euclidean quantum field theory is equivalent to the equilibrium statistical mechanics of classical fields in 4+1 dimensions at temperature h. It is well known in statistical mechanics that the theory of systems at fixed temperature is embedded within the more general and fundamental theory of systems at fixed energy. We therefore develop, in precise analogy, a fixed action (macrocanonical) formulation of quantum field theory. For the case of ordinary renormalizable field theories, we show (with one exception) that the microcanonical is entirely equivalent to the canonical formulation. That is, for some particular fixed value of the total action, the Green's functions of the microcanonical theory are equal, in the bulk limit, to those of the canonical theory. The microcanonical perturbation expansion is developed in some detail for lambdaphi 4 . The particular value of the action for which the two formulations are equivalent can be calculated to all orders in perturbation theory. We prove, using Lehmann's Theorem, that this value is one-half Planck unit per degree of freedom, if fermionic degrees of freedom are counted negatively. This is the 4+1 dimensional analog of the equipartition theorem. The one exception to this is supersymmetric theories. A microcanonical formulation exists if and only if supersymmetry is broken. In statistical mechanics and in field theory there are systems for which the canonical description is pathological, but the microcanonical is not. An example of such a field theory is found in one dimension. A semiclassical expansion of the microcanonical theory is well defined, while an expansion of the canonical theory is hoplessly divergent

Hamiltonians and variational principles for Alfvén simple waves

International Nuclear Information System (INIS)

Webb, G M; Hu, Q; Roux, J A le; Dasgupta, B; Zank, G P

2012-01-01

The evolution equations for the magnetic field induction B with the wave phase for Alfvén simple waves are expressed as variational principles and in the Hamiltonian form. The evolution of B with the phase (which is a function of the space and time variables) depends on the generalized Frenet–Serret equations, in which the wave normal n (which is a function of the phase) is taken to be tangent to a curve X, in a 3D Cartesian geometry vector space. The physical variables (the gas density, fluid velocity, gas pressure and magnetic field induction) in the wave depend only on the phase. Three approaches are developed. One approach exploits the fact that the Frenet equations may be written as a 3D Hamiltonian system, which can be described using the Nambu bracket. It is shown that B as a function of the phase satisfies a modified version of the Frenet equations, and hence the magnetic field evolution equations can be expressed in the Hamiltonian form. A second approach develops an Euler–Poincaré variational formulation. A third approach uses the Frenet frame formulation, in which the hodograph of B moves on a sphere of constant radius and uses a stereographic projection transformation due to Darboux. The equations for the projected field components reduce to a complex Riccati equation. By using a Cole–Hopf transformation, the Riccati equation reduces to a linear second order differential equation for the new variable. A Hamiltonian formulation of the second order differential equation then allows the system to be written in the Hamiltonian form. Alignment dynamics equations for Alfvén simple waves give rise to a complex Riccati equation or, equivalently, to a quaternionic Riccati equation, which can be mapped onto the Riccati equation obtained by stereographic projection. (paper)

Introduction to gauge field theory

International Nuclear Information System (INIS)

Bailin, D.; Love, A.

1986-01-01

This book provides a postgraduate level introduction to gauge field theory entirely from a path integral standpoint without any reliance on the more traditional method of canonical quantisation. The ideas are developed by quantising the self-interacting scalar field theory, and are then used to deal with all the gauge field theories relevant to particle physics, quantum electrodynamics, quantum chromodynamics, electroweak theory, grand unified theories, and field theories at non-zero temperature. The use of these theories to make precise experimental predictions requires the development of the renormalised theories. This book provides a knowledge of relativistic quantum mechanics, but not of quantum field theory. The topics covered form a foundation for a knowledge of modern relativistic quantum field theory, providing a comprehensive coverage with emphasis on the details of actual calculations rather than the phenomenology of the applications

Introduction to gauge field theory

International Nuclear Information System (INIS)

Bailin, David; Love, Alexander

1986-01-01

The book is intended as an introduction to gauge field theory for the postgraduate student of theoretical particle physics. The topics discussed in the book include: path integrals, classical and quantum field theory, scattering amplitudes, feynman rules, renormalisation, gauge field theories, spontaneous symmetry breaking, grand unified theory, and field theories at finite temperature. (UK)

Interest rates in quantum finance: the Wilson expansion and Hamiltonian.

Science.gov (United States)

Baaquie, Belal E

2009-10-01

Interest rate instruments form a major component of the capital markets. The Libor market model (LMM) is the finance industry standard interest rate model for both Libor and Euribor, which are the most important interest rates. The quantum finance formulation of the Libor market model is given in this paper and leads to a key generalization: all the Libors, for different future times, are imperfectly correlated. A key difference between a forward interest rate model and the LMM lies in the fact that the LMM is calibrated directly from the observed market interest rates. The short distance Wilson expansion [Phys. Rev. 179, 1499 (1969)] of a Gaussian quantum field is shown to provide the generalization of Ito calculus; in particular, the Wilson expansion of the Gaussian quantum field A(t,x) driving the Libors yields a derivation of the Libor drift term that incorporates imperfect correlations of the different Libors. The logarithm of Libor phi(t,x) is defined and provides an efficient and compact representation of the quantum field theory of the Libor market model. The Lagrangian and Feynman path integrals of the Libor market model of interest rates are obtained, as well as a derivation given by its Hamiltonian. The Hamiltonian formulation of the martingale condition provides an exact solution for the nonlinear drift of the Libor market model. The quantum finance formulation of the LMM is shown to reduce to the industry standard Bruce-Gatarek-Musiela-Jamshidian model when the forward interest rates are taken to be exactly correlated.

Studies in quantum field theory

International Nuclear Information System (INIS)

Bender, C.M.; Mandula, J.E.; Shrauner, J.E.

1982-01-01

Washington University is currently conducting research in many areas of high energy theoretical and mathematical physics. These areas include: strong-coupling approximation; classical solutions of non-Abelian gauge theories; mean-field approximation in quantum field theory; path integral and coherent state representations in quantum field theory; lattice gauge calculations; the nature of perturbation theory in large orders; quark condensation in QCD; chiral symmetry breaking; the l/N expansion in quantum field theory; effective potential and action in quantum field theories, including QCD

Noncanonical Hamiltonian density formulation of hydrodynamics and ideal MHD

International Nuclear Information System (INIS)

Morrison, P.J.; Greene, J.M.

1980-04-01

A new Hamiltonian density formulation of a perfect fluid with or without a magnetic field is presented. Contrary to previous work the dynamical variables are the physical variables, rho, v, B, and s, which form a noncanonical set. A Poisson bracket which satisfies the Jacobi identity is defined. This formulation is transformed to a Hamiltonian system where the dynamical variables are the spatial Fourier coefficients of the fluid variables

Integrable and nonintegrable Hamiltonian systems

International Nuclear Information System (INIS)

Percival, I.

1986-01-01

Traditionally Hamiltonian systems with a finite number of degrees of freedom have been divided into those with few degrees of freedom which were supposed to exhibit some kind of regular ordered motions and those with large numbers of degrees of freedom for which the methods of statistical mechanics should be used. The last few decades have seen a complete change of view. The change of view affects almost all the practical applications, particularly in mathematical physics, which has been dominated for many decades by linear mathematics, coming from quantum theory. The authors consider how this change of view affects some specific applications of dynamics and also the relation between dynamical theory and applications

A new approach in the design of an interactive environment for teaching Hamiltonian digraphs

International Nuclear Information System (INIS)

Iordan, A E; Panoiu, M

2014-01-01

In this article the authors present the necessary steps in object orientated design of an interactive environment that is dedicated to the process of acquaintances assimilation in Hamiltonian graphs theory domain, especially for the simulation of algorithms which determine the Hamiltonian trails and circuits. The modelling of the interactive environment is achieved through specific UML diagrams representing the steps of analysis, design and implementation. This interactive environment is very useful for both students and professors, because computer programming domain, especially digraphs theory domain is comprehended and assimilated with difficulty by students

Engineering field theory

CERN Document Server

Baden Fuller, A J

2014-01-01

Engineering Field Theory focuses on the applications of field theory in gravitation, electrostatics, magnetism, electric current flow, conductive heat transfer, fluid flow, and seepage.The manuscript first ponders on electric flux, electrical materials, and flux function. Discussions focus on field intensity at the surface of a conductor, force on a charged surface, atomic properties, doublet and uniform field, flux tube and flux line, line charge and line sink, field of a surface charge, field intensity, flux density, permittivity, and Coulomb's law. The text then takes a look at gravitation

Symplectic topology of integrable Hamiltonian systems

International Nuclear Information System (INIS)

Nguyen Tien Zung.

1993-08-01

We study the topology of integrable Hamiltonian systems, giving the main attention to the affine structure of their orbit spaces. In particular, we develop some aspects of Fomenko's theory about topological classification of integrable non-degenerate systems, and consider some relations between such systems and ''pure'' contact and symplectic geometry. We give a notion of integrable surgery and use it to obtain some interesting symplectic structures. (author). Refs, 10 figs

Modified weak energy condition for the energy momentum tensor in quantum field theory

International Nuclear Information System (INIS)

Latorre, J.

1998-01-01

The weak energy condition is known to fail in general when applied to expectation values of the energy momentum tensor in flat space quantum field theory. It is shown how the usual counter arguments against its validity are no longer applicable if the states vertical stroke ψ right angle for which the expectation value is considered are restricted to a suitably defined subspace. A possible natural restriction on vertical stroke ψ right angle is suggested and illustrated by two quantum mechanical examples based on a simple perturbed harmonic oscillator Hamiltonian. The proposed alternative quantum weak energy condition is applied to states formed by the action of the scalar, vector and the energy momentum tensor operators on the vacuum. We assume conformal invariance in order to determine almost uniquely three-point functions involving the energy momentum tensor in terms of a few parameters. The positivity conditions lead to non-trivial inequalities for these parameters. They are satisfied in free field theories, except in one case for dimensions close to two. Further restrictions on vertical stroke ψ right angle are suggested which remove this problem. The inequalities which follow from considering the state formed by applying the energy momentum tensor to the vacuum are shown to imply that the coefficient of the topological term in the expectation value of the trace of the energy momentum tensor in an arbitrary curved space background is positive, in accord with calculations in free field theories. (orig.)

On the embedding of quantum field theory on curved spacetimes into loop quantum gravity

International Nuclear Information System (INIS)

Stottmeister, Alexander

2015-01-01

The main theme of this thesis is an investigation into possible connections between loop quantum gravity and quantum field theory on curved spacetimes: On the one hand, we aim for the formulation of a general framework that allows for a derivation of quantum field theory on curved spacetimes in a semi-classical limit. On the other hand, we discuss representation-theoretical aspects of loop quantum gravity and quantum field theory on curved spacetimes as both of the latter presumably influence each other in the aforesaid semi-classical limit. Regarding the first point, we investigate the possible implementation of the Born-Oppenheimer approximation in the sense of space-adiabatic perturbation theory in models of loop quantum gravity-type. In the course of this, we argue for the need of a Weyl quantisation and an associated symbolic calculus for loop quantum gravity, which we then successfully define, at least to a certain extent. The compactness of the Lie groups, which models a la loop quantum gravity are based on, turns out to be a main obstacle to a fully satisfactory definition of a Weyl quantisation. Finally, we apply our findings to some toy models of linear scalar quantum fields on quantum cosmological spacetimes and discuss the implementation of space-adiabatic perturbation theory therein. In view of the second point, we start with a discussion of the microlocal spectrum condition for quantum fields on curved spacetimes and how it might be translated to a background-independent Hamiltonian quantum theory of gravity, like loop quantum gravity. The relevance of this lies in the fact that the microlocal spectrum condition selects a class of physically relevant states of the quantum matter fields and is, therefore, expected to play an important role in the aforesaid semi-classical limit of gravity-matter systems. Following this, we switch our perspective and analyse the representation theory of loop quantum gravity. We find some intriguing relations between the

Hamiltonian Algorithm Sound Synthesis

OpenAIRE

大矢, 健一

2013-01-01

Hamiltonian Algorithm (HA) is an algorithm for searching solutions is optimization problems. This paper introduces a sound synthesis technique using Hamiltonian Algorithm and shows a simple example. "Hamiltonian Algorithm Sound Synthesis" uses phase transition effect in HA. Because of this transition effect, totally new waveforms are produced.

Asymptotic behavior and Hamiltonian analysis of anti-de Sitter gravity coupled to scalar fields

International Nuclear Information System (INIS)

Henneaux, Marc; Martinez, Cristian; Troncoso, Ricardo; Zanelli, Jorge

2007-01-01

We examine anti-de Sitter gravity minimally coupled to a self-interacting scalar field in D>=4 dimensions when the mass of the scalar field is in the range m * 2 = 2 * 2 +l -2 . Here, l is the AdS radius, and m * 2 is the Breitenlohner-Freedman mass. We show that even though the scalar field generically has a slow fall-off at infinity which back reacts on the metric so as to modify its standard asymptotic behavior, one can still formulate asymptotic conditions (i) that are anti-de Sitter invariant; and (ii) that allows the construction of well-defined and finite Hamiltonian generators for all elements of the anti-de Sitter algebra. This requires imposing a functional relationship on the coefficients a, b that control the two independent terms in the asymptotic expansion of the scalar field. The anti-de Sitter charges are found to involve a scalar field contribution. Subtleties associated with the self-interactions of the scalar field as well as its gravitational back reaction, not discussed in previous treatments, are explicitly analyzed. In particular, it is shown that the fields develop extra logarithmic branches for specific values of the scalar field mass (in addition to the known logarithmic branch at the B-F bound)

The Artificial Hamiltonian, First Integrals, and Closed-Form Solutions of Dynamical Systems for Epidemics

Science.gov (United States)

Naz, Rehana; Naeem, Imran

2018-03-01

The non-standard Hamiltonian system, also referred to as a partial Hamiltonian system in the literature, of the form {\\dot q^i} = {partial H}/{partial {p_i}},\\dot p^i = - {partial H}/{partial {q_i}} + {Γ ^i}(t,{q^i},{p_i}) appears widely in economics, physics, mechanics, and other fields. The non-standard (partial) Hamiltonian systems arise from physical Hamiltonian structures as well as from artificial Hamiltonian structures. We introduce the term `artificial Hamiltonian' for the Hamiltonian of a model having no physical structure. We provide here explicitly the notion of an artificial Hamiltonian for dynamical systems of ordinary differential equations (ODEs). Also, we show that every system of second-order ODEs can be expressed as a non-standard (partial) Hamiltonian system of first-order ODEs by introducing an artificial Hamiltonian. This notion of an artificial Hamiltonian gives a new way to solve dynamical systems of first-order ODEs and systems of second-order ODEs that can be expressed as a non-standard (partial) Hamiltonian system by using the known techniques applicable to the non-standard Hamiltonian systems. We employ the proposed notion to solve dynamical systems of first-order ODEs arising in epidemics.

Nonlinear Lorentz-invariant theory of gravitation

International Nuclear Information System (INIS)

Petry, W.

1976-01-01

A nonlinear Lorentz-invariant theory of gravitation and a Lorentz-invariant Hamiltonian for a particle with spin in the gravitational field are developed. The equations of motions are studied. The theory is applied to the three well known tests of General Relativity. In the special case of the red shift of spectral lines and of the deflection of light, the theory gives the same results as the General Theory of Relativity, whereas in the case of the perihelion of the Mercury, the theory gives 40,3'', in good agreement with experimental results of Dicke. (author)

Quantum field theory

CERN Document Server

Mandl, Franz

2010-01-01

Following on from the successful first (1984) and revised (1993) editions, this extended and revised text is designed as a short and simple introduction to quantum field theory for final year physics students and for postgraduate students beginning research in theoretical and experimental particle physics. The three main objectives of the book are to: Explain the basic physics and formalism of quantum field theory To make the reader proficient in theory calculations using Feynman diagrams To introduce the reader to gauge theories, which play a central role in elementary particle physic

Dual double field theory

Energy Technology Data Exchange (ETDEWEB)

Bergshoeff, Eric A. [Centre for Theoretical Physics, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Hohm, Olaf [Simons Center for Geometry and Physics, Stony Brook University,Stony Brook, NY 11794-3636 (United States); Penas, Victor A. [Centre for Theoretical Physics, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Riccioni, Fabio [INFN - Sezione di Roma, Dipartimento di Fisica, Università di Roma “La Sapienza”,Piazzale Aldo Moro 2, 00185 Roma (Italy)

2016-06-06

We present the dual formulation of double field theory at the linearized level. This is a classically equivalent theory describing the duals of the dilaton, the Kalb-Ramond field and the graviton in a T-duality or O(D,D) covariant way. In agreement with previous proposals, the resulting theory encodes fields in mixed Young-tableau representations, combining them into an antisymmetric 4-tensor under O(D,D). In contrast to previous proposals, the theory also requires an antisymmetric 2-tensor and a singlet, which are not all pure gauge. The need for these additional fields is analogous to a similar phenomenon for “exotic' dualizations, and we clarify this by comparing with the dualizations of the component fields. We close with some speculative remarks on the significance of these observations for the full non-linear theory yet to be constructed.

Nonlocal continuum field theories

CERN Document Server

2002-01-01

Nonlocal continuum field theories are concerned with material bodies whose behavior at any interior point depends on the state of all other points in the body -- rather than only on an effective field resulting from these points -- in addition to its own state and the state of some calculable external field. Nonlocal field theory extends classical field theory by describing the responses of points within the medium by functionals rather than functions (the "constitutive relations" of classical field theory). Such considerations are already well known in solid-state physics, where the nonlocal interactions between the atoms are prevalent in determining the properties of the material. The tools developed for crystalline materials, however, do not lend themselves to analyzing amorphous materials, or materials in which imperfections are a major part of the structure. Nonlocal continuum theories, by contrast, can describe these materials faithfully at scales down to the lattice parameter. This book presents a unif...

Morse theory interpretation of topological quantum field theories

International Nuclear Information System (INIS)

Labastida, J.M.F.

1989-01-01

Topological quantum field theories are interpreted as a generalized form of Morse theory. This interpretation is applied to formulate the simplest topological quantum field theory: Topological quantum mechanics. The only non-trivial topological invariant corresponding to this theory is computed and identified with the Euler characteristic. Using field theoretical methods this topological invariant is calculated in different ways and in the process a proof of the Gauss-Bonnet-Chern-Avez formula as well as some results of degenerate Morse theory are obtained. (orig.)

Hamiltonian Monte Carlo study of the N=1 Wess-Zumino model on the lattice in 1+1 dimensions

International Nuclear Information System (INIS)

Schiller, A.

1984-01-01

1+1 dimensional models with restricted supersymmetry are studied. The problems of formulating supersymmetric models on the lattice are overcome by working in the Hamiltonian lattice formulation and using restricted supersymmetry algebra involving only the Hamiltonian. For the two-dimensional Wess-Zumino model a lattice Hamiltonian suitable for the local Hamiltonian method is obtained. Using this method field theoretical models with fermions and scalar Higgs fields are investigated. Emphasis is laid on supersymmetry breaking and soliton formation

Identity of the SU(3) model phenomenological hamiltonian and the hamiltonian of nonaxial rotator

International Nuclear Information System (INIS)

Filippov, G.F.; Avramenko, V.I.; Sokolov, A.M.

1984-01-01

Interpretation of nonspheric atomic nuclei spectra on the basis of phenomenological hamiltonians of SU(3) model showed satisfactory agreement of simulation calculations with experimental data. Meanwhile physical sense of phenomenological hamiltonians was not yet discussed. It is shown that phenomenological hamiltonians of SU(3) model are reduced to hamiltonian of nonaxial rotator but with additional items of the third and fourth powers angular momentum operator of rotator

Axiomatic conformal field theory

International Nuclear Information System (INIS)

Gaberdiel, M.R.; Goddard, P.

2000-01-01

A new rigourous approach to conformal field theory is presented. The basic objects are families of complex-valued amplitudes, which define a meromorphic conformal field theory (or chiral algebra) and which lead naturally to the definition of topological vector spaces, between which vertex operators act as continuous operators. In fact, in order to develop the theory, Moebius invariance rather than full conformal invariance is required but it is shown that every Moebius theory can be extended to a conformal theory by the construction of a Virasoro field. In this approach, a representation of a conformal field theory is naturally defined in terms of a family of amplitudes with appropriate analytic properties. It is shown that these amplitudes can also be derived from a suitable collection of states in the meromorphic theory. Zhu's algebra then appears naturally as the algebra of conditions which states defining highest weight representations must satisfy. The relationship of the representations of Zhu's algebra to the classification of highest weight representations is explained. (orig.)

Hamiltonian formalism for perfect fluids in general relativity

International Nuclear Information System (INIS)

Demaret, J.; Moncrief, V.

1980-01-01

Schutz's Hamiltonian theory of a relativistic perfect fluid, based on the velocity-potential version of classical perfect fluid hydrodynamics as formulated by Seliger and Whitham, is used to derive, in the framework of the Arnowitt, Deser, and Misner (ADM) method, a general partially reduced Hamiltonian for relativistic systems filled with a perfect fluid. The time coordinate is chosen, as in Lund's treatment of collapsing balls of dust, as minus the only velocity potential different from zero in the case of an irrotational and isentropic fluid. A ''semi-Dirac'' method can be applied to quantize astrophysical and cosmological models in the framework of this partially reduced formalism. If one chooses Taub's adapted comoving coordinate system, it is possible to derive a fully reduced ADM Hamiltonian, which is equal to minus the total baryon number of the fluid, generalizing a result previously obtained by Moncrief in the more particular framework of Taub's variational principle, valid for self-gravitating barotropic relativistic perfect fluids. An unconstrained Hamiltonian density is then explicitly derived for a fluid obeying the equation of state p=(gamma-1)rho (1 < or = γ < or = 2), which can adequately describe the phases of very high density attained in a catastrophic collapse or during the early stages of the Universe. This Hamiltonian density, shown to be equivalent to Moncrief's in the particular case of an isentropic fluid, can be simplified for fluid-filled class-A diagonal Bianchi-type cosmological models and appears as a suitable starting point for the study of the canonical quantization of these models

On asymptotic solutions of Regge field theory in zero transverse dimensions

International Nuclear Information System (INIS)

Bondarenko, S.; Horwitz, L.; Levitan, J.; Yahalom, A.

2013-01-01

An investigation of dynamical properties of solutions of a toy model of interacting Pomerons with triple vertex in zero transverse dimension is performed. Stable points and corresponding solutions at the limit of large rapidity are studied in the framework of a given model. It is shown that, at large rapidity, the “fan” amplitude is also a leading solution for the full RFT-0 (Regge Field Theory in zero transverse dimensions) Hamiltonian with both vertices of Pomeron splitting and merging included. An analytical form of the symmetrical solution of the equations of motion at high energy is obtained as well. For the solutions we have found, the scattering amplitude at large values of rapidity is calculated. Stability of the solutions is investigated by Lyapunov functions and the presence of closed cycles in solutions is demonstrated by the new method