Hamiltonian Formalism

Hamiltonian Aspects of Three-Layer Stratified Fluids

Journal of Nonlinear Science ◽

10.1007/s00332-021-09726-0 ◽

2021 ◽

Vol 31 (4) ◽

Author(s):

R. Camassa ◽

G. Falqui ◽

G. Ortenzi ◽

M. Pedroni ◽

T. T. Vu Ho

Keyword(s):

Hamiltonian Structure ◽

Linear Equations ◽

Hamiltonian Formalism ◽

Reduction Process ◽

Ideal Fluids ◽

Upper Lid ◽

Stratification Structure ◽

Special Solutions ◽

Dispersionless Limit ◽

Unbounded Fluid

AbstractThe theory of three-layer density-stratified ideal fluids is examined with a view toward its generalization to the n-layer case. The focus is on structural properties, especially for the case of a rigid upper lid constraint. We show that the long-wave dispersionless limit is a system of quasi-linear equations that do not admit Riemann invariants. We equip the layer-averaged one-dimensional model with a natural Hamiltonian structure, obtained with a suitable reduction process from the continuous density stratification structure of the full two-dimensional equations proposed by Benjamin. For a laterally unbounded fluid between horizontal rigid boundaries, the paradox about the non-conservation of horizontal total momentum is revisited, and it is shown that the pressure imbalances causing it can be intensified by three-layer setups with respect to their two-layer counterparts. The generator of the x-translational symmetry in the n-layer setup is also identified by the appropriate Hamiltonian formalism. The Boussinesq limit and a family of special solutions recently introduced by de Melo Viríssimo and Milewski are also discussed.

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Hamiltonian formalism for Euler parameters

Celestial Mechanics and Dynamical Astronomy ◽

10.1007/bf01230340 ◽

1985 ◽

Vol 37 (1) ◽

pp. 47-57 ◽

Cited By ~ 13

Author(s):

Andrzej J. Maciejewski

Keyword(s):

Hamiltonian Formalism ◽

Euler Parameters

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INDICATIONS OF A ΔI=1/2 RULE IN THE STRONG COUPLING REGIME

International Journal of Modern Physics A ◽

10.1142/s0217751x8800059x ◽

1988 ◽

Vol 03 (06) ◽

pp. 1385-1412

Author(s):

IAN G. ANGUS

Keyword(s):

Lattice Qcd ◽

Strong Coupling ◽

Computer Algebra ◽

Free Parameter ◽

Hamiltonian Formalism ◽

Strong Coupling Expansion ◽

Calculation Scheme ◽

Strong Coupling Regime ◽

Weak Decays ◽

The One

We will attempt to understand the ΔI=1/2 pattern of the nonleptonic weak decays of the kaons. The calculation scheme employed is the Strong Coupling Expansion of lattice QCD. Kogut-Susskind fermions are used in the Hamiltonian formalism. We will describe in detail the methods used to expedite this calculation, all of which was done by computer algebra. The final result is very encouraging. Even though an exact interpretation is clouded by the presence of irrelevant operators, and questions of lattice artifacts, a signal of the ΔI=1/2 rule appears to be observable. With an appropriate choice of the one free parameter, enhancements greater than those observed experimentally can be obtained. We also point out a number of surprising results which we turn up in the course of the calculation.

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Finite BRST–anti-BRST transformations in generalized Hamiltonian formalism

International Journal of Modern Physics A ◽

10.1142/s0217751x14501590 ◽

2014 ◽

Vol 29 (27) ◽

pp. 1450159 ◽

Cited By ~ 11

Author(s):

Pavel Yu. Moshin ◽

Alexander A. Reshetnyak

Keyword(s):

Dynamical Systems ◽

Path Integral ◽

Hamiltonian Path ◽

Hamiltonian Formalism ◽

Lagrangian Formalism ◽

Yang Mills ◽

Gauge Dependence ◽

Field Dependent ◽

Gauge Fixing ◽

Constrained Dynamical Systems

We introduce the notion of finite BRST–anti-BRST transformations for constrained dynamical systems in the generalized Hamiltonian formalism, both global and field-dependent, with a doublet λa, a = 1, 2, of anticommuting Grassmann parameters and find explicit Jacobians corresponding to these changes of variables in the path integral. It turns out that the finite transformations are quadratic in their parameters. Exactly as in the case of finite field-dependent BRST–anti-BRST transformations for the Yang–Mills vacuum functional in the Lagrangian formalism examined in our previous paper [arXiv:1405.0790 [hep-th]], special field-dependent BRST–anti-BRST transformations with functionally-dependent parameters λa= ∫ dt(saΛ), generated by a finite even-valued function Λ(t) and by the anticommuting generators saof BRST–anti-BRST transformations, amount to a precise change of the gauge-fixing function for arbitrary constrained dynamical systems. This proves the independence of the vacuum functional under such transformations. We derive a new form of the Ward identities, depending on the parameters λaand study the problem of gauge dependence. We present the form of transformation parameters which generates a change of the gauge in the Hamiltonian path integral, evaluate it explicitly for connecting two arbitrary Rξ-like gauges in the Yang–Mills theory and establish, after integration over momenta, a coincidence with the Lagrangian path integral [arXiv:1405.0790 [hep-th]], which justifies the unitarity of the S-matrix in the Lagrangian approach.

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Actions, topological terms and boundaries in first-order gravity: A review

International Journal of Modern Physics D ◽

10.1142/s0218271816300111 ◽

2016 ◽

Vol 25 (04) ◽

pp. 1630011 ◽

Cited By ~ 19

Author(s):

Alejandro Corichi ◽

Irais Rubalcava-García ◽

Tatjana Vukašinac

Keyword(s):

Boundary Conditions ◽

Symplectic Structure ◽

Equations Of Motion ◽

Hamiltonian Formalism ◽

Action Principle ◽

Internal Boundary ◽

Four Dimensions ◽

First Order ◽

Conserved Charges ◽

Boundary Terms

In this review, we consider first-order gravity in four dimensions. In particular, we focus our attention in formulations where the fundamental variables are a tetrad [Formula: see text] and a [Formula: see text] connection [Formula: see text]. We study the most general action principle compatible with diffeomorphism invariance. This implies, in particular, considering besides the standard Einstein–Hilbert–Palatini term, other terms that either do not change the equations of motion, or are topological in nature. Having a well defined action principle sometimes involves the need for additional boundary terms, whose detailed form may depend on the particular boundary conditions at hand. In this work, we consider spacetimes that include a boundary at infinity, satisfying asymptotically flat boundary conditions and/or an internal boundary satisfying isolated horizons boundary conditions. We focus on the covariant Hamiltonian formalism where the phase space [Formula: see text] is given by solutions to the equations of motion. For each of the possible terms contributing to the action, we consider the well-posedness of the action, its finiteness, the contribution to the symplectic structure, and the Hamiltonian and Noether charges. For the chosen boundary conditions, standard boundary terms warrant a well posed theory. Furthermore, the boundary and topological terms do not contribute to the symplectic structure, nor the Hamiltonian conserved charges. The Noether conserved charges, on the other hand, do depend on such additional terms. The aim of this manuscript is to present a comprehensive and self-contained treatment of the subject, so the style is somewhat pedagogical. Furthermore, along the way, we point out and clarify some issues that have not been clearly understood in the literature.

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Variational formulation of relativistic four-body systems in quantum field theory: scalar quadronium

Canadian Journal of Physics ◽

10.1139/p02-061 ◽

2002 ◽

Vol 80 (5) ◽

pp. 605-612

Author(s):

B Ding ◽

J W Darewych

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Fock Space ◽

Hamiltonian Formalism ◽

Massless Scalar ◽

Massless Scalar Field ◽

Quantum Field ◽

Scalar Particles ◽

Pairwise Interactions ◽

Approximate Wave

We discuss a variational method for describing relativistic four-body systems within the Hamiltonian formalism of quantum field theory. The scalar Yukawa (or WickCutkosky) model, in which scalar particles and antiparticles interact via a massive or massless scalar field, is used to illustrate the method. A Fock-space variational trial state is used to describe the stationary states of scalar quadronium (two particles and two antiparticles) interacting via one-quantum exchange and virtual annihilation pairwise interactions. Numerical results for the ground-state mass and approximate wave functions of quadronium are presented for various strengths of the coupling, for the massive and massless quantum exchange cases. PACS Nos.: 11.10Ef, 11.10St, 03.70+k, 03.65Pm

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A simple approach to the state-specific MR-CC using the intermediate Hamiltonian formalism

The Journal of Chemical Physics ◽

10.1063/1.4940781 ◽

2016 ◽

Vol 144 (6) ◽

pp. 064101 ◽

Cited By ~ 10

Author(s):

E. Giner ◽

G. David ◽

A. Scemama ◽

J. P. Malrieu

Keyword(s):

Hamiltonian Formalism ◽

Simple Approach ◽

The State

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GENERAL COVARIANCE, TOPOLOGICAL QUANTUM FIELD THEORIES AND FRACTIONAL STATISTICS

International Journal of Modern Physics A ◽

10.1142/s0217751x92000144 ◽

1992 ◽

Vol 07 (02) ◽

pp. 209-234 ◽

Cited By ~ 1

Author(s):

J. GAMBOA

Keyword(s):

Hamiltonian Formalism ◽

Field Theories ◽

General Covariance ◽

Quantum Field Theories ◽

Quantum Field ◽

Fractional Statistics ◽

Multiply Connected ◽

Topological Quantum ◽

Gauge Fixing ◽

Topological Quantum Field Theories

Topological quantum field theories and fractional statistics are both defined in multiply connected manifolds. We study the relationship between both theories in 2 + 1 dimensions and we show that, due to the multiply-connected character of the manifold, the propagator for any quantum (field) theory always contains a first order pole that can be identified with a physical excitation with fractional spin. The article starts by reviewing the definition of general covariance in the Hamiltonian formalism, the gauge-fixing problem and the quantization following the lines of Batalin, Fradkin and Vilkovisky. The BRST–BFV quantization is reviewed in order to understand the topological approach proposed here.

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