GAUGE INVARIANCE AND CONSTRAINTS

1989 ◽  
Vol 04 (13) ◽  
pp. 3211-3228 ◽  
Author(s):  
P.N. PYATOV ◽  
A.V. RAZUMOV
Keyword(s):  
Phase Space ◽  
Wide Class ◽  
Gauge Invariance ◽  
Lagrangian Systems ◽  
Poisson Brackets ◽  
Hamiltonian Description ◽  
Gauge Invariant ◽  
Primary Constraint ◽  
Extension Of Functions ◽  
Constraint Surface

It is shown that in the Hamiltonian description of a wide class of gauge invariant Lagrangian systems there arise only primary and secondary constraints and they are all first class. The explicit expressions for the Poisson brackets of the Hamiltonian and the constraints are obtained by introducing the so-called “standard” extension of functions originally defined on the primary constraint surface to the whole phase space.

GAUGE INVARIANCE AND CONSTRAINTS: OPEN GAUGE ALGEBRAS

1992 ◽  
Vol 07 (22) ◽  
pp. 5549-5561 ◽  
Author(s):  
KH. S. NIROV ◽  
P.N. PYATOV ◽  
A.V. RAZUMOV
Keyword(s):  
Wide Class ◽  
Gauge Invariance ◽  
Poisson Brackets ◽  
Hamiltonian Description ◽  
Gauge Invariant

For a wide class of gauge-invariant systems with open gauge algebras the Hamiltonian description is constructed and the Poisson brackets of the constraints are calculated. It is shown that in the case under consideration there arise only first class constraints.

scholarly journals CONSTRAINT ALGEBRAS IN GAUGE-INVARIANT SYSTEMS

1995 ◽  
Vol 10 (28) ◽  
pp. 4087-4105 ◽  
Author(s):  
KH. S. NIROV
Keyword(s):  
Wide Class ◽  
Arbitrary Function ◽  
Arbitrary Order ◽  
Local Symmetry ◽  
Poisson Brackets ◽  
Hamiltonian Description ◽  
Gauge Invariant ◽  
Symmetry Transformations ◽  
Constraint Algebra ◽  
Derivatives Of

A Hamiltonian description is constructed for a wide class of mechanical systems having local symmetry transformations depending on time derivatives of the gauge parameters of arbitrary order. The Poisson brackets of the Hamiltonian and constraints with each other and with an arbitrary function are explicitly obtained. The constraint algebra is proved to be of the first class.

scholarly journals DUALITY THROUGH THE SYMPLECTIC EMBEDDING FORMALISM

2007 ◽  
Vol 22 (21) ◽  
pp. 3605-3620 ◽  
Author(s):  
E. M. C. ABREU ◽  
A. C. R. MENDES ◽  
C. NEVES ◽  
W. OLIVEIRA ◽  
F. I. TAKAKURA
Keyword(s):  
Phase Space ◽  
Gauge Invariance ◽  
Zero Mode ◽  
Mass Term ◽  
Gauge Invariant ◽  
Embedding Method ◽  
Symplectic Embedding ◽  
The One ◽  
Topological Term

In this work we show that we can obtain dual equivalent actions following the symplectic formalism with the introduction of extra variables which enlarge the phase space. We show that the results are equal as the one obtained with the recently developed gauging iterative Noether dualization method. We believe that, with the arbitrariness property of the zero mode, the symplectic embedding method is more profound since it can reveal a whole family of dual equivalent actions. We illustrate the method demonstrating that the gauge-invariance of the electromagnetic Maxwell Lagrangian broken by the introduction of an explicit mass term and a topological term can be restored to obtain the dual equivalent and gauge-invariant version of the theory.

scholarly journals HAMILTONIAN DESCRIPTION OF SINGULAR LAGRANGIAN SYSTEMS WITH SPONTANEOUSLY BROKEN TIME TRANSLATION SYMMETRY

2013 ◽  
Vol 28 (05) ◽  
pp. 1350002 ◽  
Author(s):  
LIU ZHAO ◽  
PENGFEI YU ◽  
WEI XU
Keyword(s):  
Phase Space ◽  
Time Reversal ◽  
Spontaneous Breaking ◽  
Lagrangian Systems ◽  
Energy Functions ◽  
Hamiltonian Description ◽  
Time Translation ◽  
Constrained Hamiltonian Systems ◽  
Translation Symmetry ◽  
The Common

Shapere and Wilczek recently found some singular Lagrangian systems which spontaneously breaks time translation symmetry. The common feature of their models is that the energy functions are multi-valued in terms of the canonical phase space variables and the symmetry breaking ground states are all located at the brunching point singularities. By enlarging the phase space and making use of Dirac's theory on constrained Hamiltonian systems, we present the Hamiltonian description of some of the models discussed by Shapere and Wilczek and found that both the multi-valuedness and the brunching point singularities can be avoided, while the spontaneous breaking of time translation becomes more transparent. It is also shown that the breaking of time translation is always accompanied by the breaking of time reversal.

scholarly journals POISSON ALGEBRA OF WILSON LOOPS IN FOUR-DIMENSIONAL YANG-MILLS THEORY

1995 ◽  
Vol 10 (17) ◽  
pp. 2479-2505 ◽  
Author(s):  
S.G. RAJEEV ◽  
O.T. TURGUT
Keyword(s):  
Phase Space ◽  
Gauge Theories ◽  
Poisson Algebra ◽  
Coadjoint Orbit ◽  
Quadratic Algebra ◽  
Wilson Loops ◽  
Poisson Brackets ◽  
Canonical Structure ◽  
Gauge Invariant ◽  
Yang Mills

We formulate the canonical structure of Yang-Mills theory in terms of Poisson brackets of gauge-invariant observables analogous to Wilson loops. This algebra is nontrivial and tractable in a light cone formulation. For U (N) gauge theories the result is a Lie algebra while for SU (N) gauge theories it is a quadratic algebra. We also study the identities satisfied by the gauge-invariant observables. We suggest that the phase space of a Yang-Mills theory is a coadjoint orbit of our Poisson algebra; some partial results in this direction are obtained.

scholarly journals The Ostrogradsky Prescription for BFV Formalism

1997 ◽  
Vol 12 (27) ◽  
pp. 1991-2004
Author(s):  
Khazret S. Nirov
Keyword(s):  
Higher Order ◽  
Gauge Invariant ◽  
Primary Constraint ◽  
Brst Charge ◽  
Higher Order Terms ◽  
Derivatives Of ◽  
Constraint Surface

Gauge-invariant systems of a general form with higher order time derivatives of gauge parameters are investigated within the framework of the BFV formalism. Higher order terms of the BRST charge and BRST-invariant Hamiltonian are obtained. It is shown that the identification rules for Lagrangian and Hamiltonian BRST ghost variables depend on the choice of the extension of constraints from the primary constraint surface.

scholarly journals EXTENDED OBSERVABLES IN HAMILTONIAN THEORIES WITH CONSTRAINTS

2001 ◽  
Vol 16 (26) ◽  
pp. 4271-4296 ◽  
Author(s):  
SIMON L. LYAKHOVICH ◽  
ROBERT MARNELIUS
Keyword(s):  
Phase Space ◽  
Differential Operators ◽  
Poisson Algebra ◽  
Dirac Bracket ◽  
Covariant Quantization ◽  
Mapping Procedure ◽  
Gauge Invariant ◽  
Hamiltonian Theory ◽  
Bracket Algebra ◽  
Constraint Surface

In a classical Hamiltonian theory with second-class constraints the phase space functions on the constraint surface are observables. We give general formulas for extended observables, which are expressions representing the observables in the enveloping unconstrained phase space. These expressions satisfy in the unconstrained phase space a Poisson algebra of the same form as the Dirac bracket algebra of the observables on the constraint surface. The general formulas involve new differential operators that differentiate the Dirac bracket. Similar extended observables are also constructed for theories with first-class constraints which, however, are gauge-dependent. For such theories one may also construct gauge-invariant extensions with similar properties. Whenever extended observables exist the theory is expected to allow for a covariant quantization. A mapping procedure is proposed for covariant quantization of theories with second-class constraints.

scholarly journals Gauge invariance, polar coordinates and inflation

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Ali Akil ◽  
Xi Tong
Keyword(s):  
Coordinate System ◽  
Effective Potential ◽  
Gauge Invariance ◽  
Polar Coordinates ◽  
Quantum Corrections ◽  
Background Current ◽  
Gauge Invariant ◽  
Gauge Dependence ◽  
Current Term ◽  
Invariant Current

Abstract We point out the necessity of resolving the apparent gauge dependence in the quantum corrections of cosmological observables for Higgs-like inflation models. We highlight the fact that this gauge dependence is due to the use of an asymmetric background current which is specific to a choice of coordinate system in the scalar manifold. Favoring simplicity over complexity, we further propose a practical shortcut to gauge-independent inflationary observables by using effective potential obtained from a polar-like background current choice. We demonstrate this shortcut for several explicit examples and present a gauge-independent prediction of inflationary observables in the Abelian Higgs model. Furthermore, with Nielsen’s gauge dependence identities, we show that for any theory to all orders, a gauge-invariant current term gives a gauge-independent effective potential and thus gauge-invariant inflationary observables.

scholarly journals A master exceptional field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Guillaume Bossard ◽  
Axel Kleinschmidt ◽  
Ergin Sezgin
Keyword(s):  
Field Theory ◽  
Gauge Invariance ◽  
Sigma Model ◽  
Linear Equations ◽  
Field Theories ◽  
Gauge Invariant ◽  
Non Linear ◽  
Non Linear Equations

Abstract We construct a pseudo-Lagrangian that is invariant under rigid E11 and transforms as a density under E11 generalised diffeomorphisms. The gauge-invariance requires the use of a section condition studied in previous work on E11 exceptional field theory and the inclusion of constrained fields that transform in an indecomposable E11-representation together with the E11 coset fields. We show that, in combination with gauge-invariant and E11-invariant duality equations, this pseudo-Lagrangian reduces to the bosonic sector of non-linear eleven-dimensional supergravity for one choice of solution to the section condi- tion. For another choice, we reobtain the E8 exceptional field theory and conjecture that our pseudo-Lagrangian and duality equations produce all exceptional field theories with maximal supersymmetry in any dimension. We also describe how the theory entails non-linear equations for higher dual fields, including the dual graviton in eleven dimensions. Furthermore, we speculate on the relation to the E10 sigma model.

scholarly journals All-plus helicity off-shell gauge invariant multigluon amplitudes at one loop

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Etienne Blanco ◽  
Andreas van Hameren ◽  
Piotr Kotko ◽  
Krzysztof Kutak
Keyword(s):  
Scattering Amplitudes ◽  
Gauge Invariance ◽  
Arbitrary Number ◽  
Gauge Invariant

Abstract We calculate one loop scattering amplitudes for arbitrary number of positive helicity on-shell gluons and one off-shell gluon treated within the quasi-multi Regge kinematics. The result is fully gauge invariant and possesses the correct on-shell limit. Our method is based on embedding the off-shell process, together with contributions needed to retain gauge invariance, in a bigger fully on-shell process with auxiliary quark or gluon line.

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