scholarly journals From the Poincaré-Cartan Form to a Gerstenhaber Algebra of Poisson Brackets in Field Theory

1995 ◽  
pp. 173-183
Author(s):  
Igor V. Kanatchikov
Keyword(s):  
Field Theory ◽  
Poisson Brackets ◽  
Cartan Form ◽  
Gerstenhaber Algebra

scholarly journals Covariant Poisson Brackets in Geometric Field Theory

2005 ◽  
Vol 256 (2) ◽  
pp. 375-410 ◽  
Author(s):  
Michael Forger ◽  
Sandro Vieira Romero
Keyword(s):  
Field Theory ◽  
Poisson Brackets

scholarly journals The sh Lie Structure of Poisson Brackets in Field Theory

1998 ◽  
Vol 191 (3) ◽  
pp. 585-601 ◽  
Author(s):  
G. Barnich ◽  
R. Fulp ◽  
T. Lada ◽  
J. Stasheff
Keyword(s):  
Field Theory ◽  
Poisson Brackets

scholarly journals A NOTE ON SCALAR FIELD THEORY IN AdS3/CFT2

2010 ◽  
Vol 25 (14) ◽  
pp. 2815-2836
Author(s):  
PABLO MINCES
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Central Charge ◽  
Virasoro Algebra ◽  
Radial Coordinate ◽  
Poisson Brackets ◽  
Scalar Field Theory ◽  
Classical Level ◽  
Conjugate Momentum ◽  
Conformal Fields

We consider a scalar field theory in AdS d+1, and introduce a formalism on surfaces at equal values of the radial coordinate. In particular, we define the corresponding conjugate momentum. We compute the Noether currents for isometries in the bulk, and perform the asymptotic limit on the corresponding charges. We then introduce Poisson brackets at the border, and show that the asymptotic values of the bulk scalar field and the conjugate momentum transform as conformal fields of scaling dimensions Δ- and Δ+, respectively, where Δ± are the standard parameters giving the asymptotic behavior of the scalar field in AdS. Then we consider the case d = 2, where we obtain two copies of the Virasoro algebra, with vanishing central charge at the classical level. An AdS3/CFT2 prescription, giving the commutators of the boundary CFT in terms of the Poisson brackets at the border, arises in a natural way. We find that the boundary CFT is similar to a generalized ghost system. We introduce two different ground states, and then compute the normal ordering constants and quantum central charges, which depend on the mass of the scalar field and the AdS radius. We discuss certain implications of the results.

scholarly journals Peierls Brackets in Field Theory

2003 ◽  
Vol 18 (12) ◽  
pp. 2033-2039 ◽  
Author(s):  
G. Bimonte ◽  
G. Esposito ◽  
G. Marmo ◽  
C. Stornaiolo
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
General Relativity ◽  
Poisson Bracket ◽  
Gauge Field ◽  
Diffeomorphism Group ◽  
Gauge Field Theory ◽  
Poisson Brackets ◽  
Quantum Field ◽  
Group Invariant

Peierls brackets are part of the space-time approach to quantum field theory, and provide a Poisson bracket which, being defined for pairs of observables which are group invariant, is group invariant by construction. It is therefore well suited for combining the use of Poisson brackets and the full diffeomorphism group in general relativity. The present paper provides an introduction to the topic, with applications to gauge field theory.

scholarly journals COVARIANT HAMILTONIAN FIELD THEORY

2008 ◽  
Vol 17 (03) ◽  
pp. 435-491 ◽  
Author(s):  
JÜRGEN STRUCKMEIER ◽  
ANDREAS REDELBACH
Keyword(s):  
Field Theory ◽  
Canonical Transformation ◽  
Generating Functions ◽  
Lagrangian Description ◽  
Poisson Brackets ◽  
Canonical Transformations ◽  
Transformation Theory ◽  
Field Equations ◽  
Time Step ◽  
Transformation Rules

A consistent, local coordinate formulation of covariant Hamiltonian field theory is presented. Whereas the covariant canonical field equations are equivalent to the Euler–Lagrange field equations, the covariant canonical transformation theory offers more general means for defining mappings that preserve the form of the field equations than the usual Lagrangian description. It is proven that Poisson brackets, Lagrange brackets, and canonical 2-forms exist that are invariant under canonical transformations of the fields. The technique to derive transformation rules for the fields from generating functions is demonstrated by means of various examples. In particular, it is shown that the infinitesimal canonical transformation furnishes the most general form of Noether's theorem. Furthermore, we specify the generating function of an infinitesimal space-time step that conforms to the field equations.

POISSON BRACKETS IN FIELD THEORY

1959 ◽  
Vol 37 (1) ◽  
pp. 5-9 ◽  
Author(s):  
Hans Freistadt
Keyword(s):  
Field Theory ◽  
Quantum Theory ◽  
Close Connection ◽  
Tensor Algebra ◽  
Poisson Brackets ◽  
Dirac Fields ◽  
Klein Gordon ◽  
Covariant Field

Poisson brackets for covariant field theory are defined in such a way as to demonstrate the close connection and ready transition between the classical brackets and the corresponding commutators of quantum theory. The approach of Good is followed in general; but the questions of tensor algebra are handled differently, requiring the introduction of a family of space-like surfaces and their normals. As an illustration, the free Klein-Gordon and Dirac fields are worked out.

The commutation laws of relativistic field theory

1952 ◽  
Vol 214 (1117) ◽  
pp. 143-157 ◽  
Keyword(s):  
Field Theory ◽  
Canonical Form ◽  
Action Principle ◽  
Poisson Brackets ◽  
Relativistic Field ◽  
Canonical Theory ◽  
Relativistic Field Theory ◽  
Dirac Particles ◽  
Canonical Variables ◽  
Definition Of

A definition of Poisson brackets is given which is related to the action principle, but does not require the introduction of canonical variables. This permits the laws for forming both the commutators of canonical theory and the anticommutators of Fermi-Dirac particles to be stated in a manifestly covariant way. Examples of the use of this method are given. The last section discusses tentatively the extension to the case of equations which cannot be written in canonical form.

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