scholarly journals General $$U(N)$$ U ( N ) Gauge Transformations in the Realm of Covariant Hamiltonian Field Theory

2013 ◽  
pp. 367-395 ◽  
Author(s):  
Jürgen Struckmeier ◽  
Hermine Reichau
Keyword(s):  
Field Theory ◽  
Gauge Transformations

scholarly journals The canonical formulation of E6(6) exceptional field theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Lars T. Kreutzer
Keyword(s):  
Field Theory ◽  
Model Theory ◽  
Kinetic Term ◽  
Gauge Invariant ◽  
Gauge Transformations ◽  
Canonical Formulation ◽  
Ashtekar Variables ◽  
Constraint Algebra ◽  
Topological Term

Abstract We investigate the canonical formulation of the (bosonic) E6(6) exceptional field theory. The explicit non-integral (not manifestly gauge invariant) topological term of E6(6) exceptional field theory is constructed and we consider the canonical formulation of a model theory based on the topological two-form kinetic term. Furthermore we construct the canonical momenta and the canonical Hamiltonian of the full bosonic E6(6) exceptional field theory. Most of the canonical gauge transformations and some parts of the canonical constraint algebra are calculated. Moreover we discuss how to translate the results canonically into the generalised vielbein formulation. We comment on the possible existence of generalised Ashtekar variables.

scholarly journals QUANTIZATION WITHOUT THE WITTEN ANOMALIES

1996 ◽  
Vol 11 (32n33) ◽  
pp. 2601-2609 ◽  
Author(s):  
T.D. KIEU
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Boundary Conditions ◽  
Path Integral ◽  
Quantum Field ◽  
Quantum Fields ◽  
Berry's Phase ◽  
Berry’S Phase ◽  
Gauge Transformations ◽  
Gauge Anomalies

It is argued that gauge anomalies are only artefacts of the conventional quantization of quantum field theory. When the Berry’s phase is taken into consideration to satisfy certain boundary conditions of the generating path integral, the gauge anomalies associated with homotopically nontrivial gauge transformations are explicitly shown to be eliminated, without any extra quantum fields introduced.

scholarly journals THE GRAPH-REPRESENTATION APPROACH TO TOPOLOGICAL FIELD THEORY IN 2 + 1 DIMENSIONS

1992 ◽  
Vol 07 (03) ◽  
pp. 563-589
Author(s):  
STEPHEN P. MARTIN
Keyword(s):  
Field Theory ◽  
Poisson Bracket ◽  
Wave Functions ◽  
Graph Representation ◽  
Commutator Algebra ◽  
Gauge Transformations ◽  
Topological Quantum ◽  
Topological Field ◽  
Definition Of ◽  
Theory Of Graphs

An alternative definition of topological quantum field theory in 2 + 1 dimensions is discussed. The fundamental objects in this approach are not gauge fields as in the usual approach, but nonlocal observables associated with graphs. The classical theory of graphs is defined by postulating a simple diagrammatic rule for computing the Poisson bracket of any two graphs. The theory is quantized by exhibiting a quantum deformation of the classical Poisson-bracket algebra, which is realized as a commutator algebra on a Hilbert space of states. The wave functions in this "graph representation" approach are functionals on an appropriate set of graphs. This is in contrast to the usual "connection representation" approach, in which the theory is defined in terms of a gauge field and the wave functions are functionals on the space of flat spatial connections modulo gauge transformations.

ADVANCES IN TERNARY AND OCTONIONIC GAUGE FIELD THEORIES

2011 ◽  
Vol 26 (18) ◽  
pp. 2997-3012 ◽  
Author(s):  
CARLOS CASTRO
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Lie Algebra ◽  
Space Time ◽  
Time Dependent ◽  
Gauge Field Theory ◽  
Gauge Fields ◽  
Gauge Transformations ◽  
Quadratic Action ◽  
Rigid Transformations

A ternary gauge field theory is explicitly constructed based on a totally antisymmetric ternary-bracket structure associated with a 3-Lie algebra. It is shown that the ternary infinitesimal gauge transformations do obey the key closure relations [δ1, δ2] = δ3. Invariant actions for the 3-Lie algebra-valued gauge fields and scalar fields are displayed. We analyze and point out the difficulties in formulating a nonassociative octonionic ternary gauge field theory based on a ternary-bracket associated with the octonion algebra and defined earlier by Yamazaki. It is shown that a Yang–Mills-like quadratic action is invariant under global (rigid) transformations involving the Yamazaki ternary octonionic bracket, and that there is closure of these global (rigid) transformations based on constant antisymmetric parameters Λab = - Λba. Promoting the latter parameters to space–time dependent ones Λab(xμ) allows one to build an octonionic ternary gauge field theory when one imposes gauge covariant constraints on the latter gauge parameters leading to field-dependent gauge parameters and nonlinear gauge transformations. In this fashion one does not spoil the gauge invariance of the quadratic action under this restricted set of gauge transformations and which are tantamount to space–time dependent scalings (homothecy) of the gauge fields.

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