WEYL FERMION FUNCTIONAL INTEGRAL AND TWO-DIMENSIONAL GAUGE THEORIES

1990 ◽  
Vol 05 (14) ◽  
pp. 2839-2851
Author(s):  
J.L. ALONSO ◽  
J.L. CORTÉS ◽  
E. RIVAS
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Functional Integral ◽  
Integral Approach ◽  
Two Dimensional ◽  
Regularization Scheme ◽  
Schwinger Model ◽  
Left Handed ◽  
Definition Of ◽  
Weyl Fermion

In the path integral approach we introduce a general regularization scheme for a Weyl fermionic measure. This allows us to study the functional integral formulation of a two-dimensional U(1) gauge theory with an arbitrary content of left-handed and right-handed fermions. A particular result is that, in contrast with a regularization of the fermionic measure based on a unique Dirac operator, by taking the Dirac fermionic measure as a product of two independent Weyl fermionic measures a consistent and unitary result can be obtained for the Chiral Schwinger Model (CSM) as a byproduct of the arbitrariness in the definition of the fermionic measure.

scholarly journals WORLDSHEET COVARIANT PATH INTEGRAL QUANTIZATION OF STRINGS

2006 ◽  
Vol 21 (32) ◽  
pp. 6525-6574 ◽  
Author(s):  
ANDRÉ VAN TONDER
Keyword(s):  
Path Integral ◽  
First Principles ◽  
Critical Dimension ◽  
Functional Integral ◽  
Integral Approach ◽  
Vertex Operators ◽  
General Covariance ◽  
Classical Transformation ◽  
Definition Of ◽  
Independent Path

We discuss a covariant functional integral approach to the quantization of the bosonic string. In contrast to approaches relying on noncovariant operator regularizations, interesting operators here are true tensor objects with classical transformation laws, even on target spaces where the theory has a Weyl anomaly. Since no implicit noncovariant gauge choices are involved in the definition of the operators, the anomaly is clearly separated from the issue of operator renormalization and can be understood in isolation, instead of infecting the latter as in other approaches. Our method is of wider applicability to covariant theories that are not Weyl invariant, but where covariant tensor operators are desired. After constructing covariantly regularized vertex operators, we define a class of background-independent path integral measures suitable for string quantization. We show how gauge invariance of the path integral implies the usual physical state conditions in a very conceptually clean way. We then discuss the construction of the BRST action from first principles, obtaining some interesting caveats relating to its general covariance. In our approach, the expected BRST related anomalies are encoded somewhat differently from other approaches. We conclude with an unusual but amusing derivation of the value D = 26 of the critical dimension.

scholarly journals Five-Dimensional Gauge Theories and Whitham–Toda Equation

1997 ◽  
Vol 12 (29) ◽  
pp. 2183-2191 ◽  
Author(s):  
Masato Hisakado
Keyword(s):  
Gauge Theory ◽  
Toda Lattice ◽  
Gauge Theories ◽  
Toda Chain ◽  
Charge Conjugation ◽  
Two Dimensional ◽  
Toda Equation ◽  
Toda Lattice Hierarchy

The five-dimensional supersymmetric SU (N) gauge theory is studied in the framework of the relativistic Toda chain. This equation can be embedded in two-dimensional Toda lattice hierarchy. This system has the conjugate structure which corresponds to the charge conjugation.

ON THE WESS-ZUMINO TERM FOR A GENERAL ANOMALOUS GAUGE THEORY WITH SECOND CLASS CONSTRAINTS

1990 ◽  
Vol 05 (06) ◽  
pp. 1123-1133 ◽  
Author(s):  
C. WOTZASEK
Keyword(s):  
Gauge Theory ◽  
Degrees Of Freedom ◽  
Gauge Theories ◽  
Vector Boson ◽  
Boson Field ◽  
Massive Vector ◽  
Schwinger Model ◽  
Working Out

We proposed an algorithm to modify anomalous gauge theories by inserting new degrees of freedom in the system which transforms the constraints from second to first class. We illustrate this technique working out the cases of a massive vector boson field and the chiral Schwinger model.

scholarly journals TWO-DIMENSIONAL CHIRAL GAUGE THEORIES IN THE SCHRÖDINGER REPRESENTATION

1990 ◽  
Vol 05 (01) ◽  
pp. 153-173 ◽  
Author(s):  
A.V. RAMALLO
Keyword(s):  
Gauge Theories ◽  
Lorentz Invariance ◽  
Collective Excitations ◽  
Clear Understanding ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
Massive Mode ◽  
Abelian Gauge ◽  
Schrödinger Representation ◽  
Left Handed

We present a quantization, in the Schrödinger representation, of a two-dimensional theory consisting of an Abelian gauge field coupled to an arbitrary number of right- and left-handed fermions. A consistent and unitary quantum theory is obtained. The gauge symmetry is broken but Lorentz invariance survives quantization. The theory contains a series of chiral massless particles and a massive mode, which can be interpreted as collective excitations of the fields that we have in the initial Lagrangian. Our formalism is quite transparent and allows a clear understanding of the consistency of the model.

VECTOR SCHWINGER MODEL WITH A PHOTON MASS TERM: GAUGE-INVARIANT REFORMULATION, OPERATOR SOLUTIONS AND HAMILTONIAN AND PATH INTEGRAL FORMULATIONS

2007 ◽  
Vol 22 (39) ◽  
pp. 2993-3001 ◽  
Author(s):  
USHA KULSHRESHTHA
Keyword(s):  
Path Integral ◽  
Quantum Electrodynamics ◽  
Mass Term ◽  
Photon Mass ◽  
Two Dimensional ◽  
Gauge Invariant ◽  
Schwinger Model ◽  
Left Handed ◽  
Stueckelberg Formalism ◽  
Massless Fermions

We consider the vector Schwinger model (VSM) describing two-dimensional electrodynamics with massless fermions, where the left-handed and right-handed fermions are coupled to the electromagnetic field with equal couplings, with a mass term for the U(1) gauge field and then study its operator solutions and the Hamiltonian and path integral formulations. We emphasize here that although the VSM has been studied in the literature rather widely but only without a photon mass term (which was a consequence of demanding the regularization for the VSM to be gauge-invariant (GI)). The VSM with a photon mass term is seen to be a gauge-noninvariant (GNI) theory. Using the standard Stueckelberg formalism we then construct a GI theory corresponding to the proposed GNI model. From this reformulated GI theory, we further recover the physical contents of the proposed GNI theory under a very special gauge choice. The theory proposed and studied here presents a new class of models in the two-dimensional quantum electrodynamics with massless fermions but with a photon mass term.

scholarly journals Functional Integral Approach to the N-Flavor Schwinger Model

1994 ◽  
Vol 233 (1) ◽  
pp. 97-124 ◽  
Author(s):  
C. Gattringer ◽  
E. Seiler
Keyword(s):  
Functional Integral ◽  
Integral Approach ◽  
Schwinger Model

Dimensional regularization and the path-integral approach to photon mass in the Schwinger model

1989 ◽  
Vol 67 (5) ◽  
pp. 515-518
Author(s):  
T. F. Treml
Keyword(s):  
Path Integral ◽  
Quantum Electrodynamics ◽  
Dimensional Regularization ◽  
Integral Approach ◽  
Coordinate Space ◽  
Photon Mass ◽  
Two Dimensional ◽  
Schwinger Model ◽  
Path Integral Approach

The derivation of the photon mass in the Schwinger model (two-dimensional quantum electrodynamics) is studied in a path-integral approach that employs a coordinate-space form of dimensional regularization. The role of the antisymmetric epsilon pseudotensor in dimensional regularization is briefly discussed. It is shown that the correct photon mass may easily be recovered by a dimensionally regularized calculation in which the epsilon pseudotensor is taken to be a purely two-dimensional quantity.

Sign in / Sign up

Export Citation Format

Share Document