NONCANONICAL FEATURES IN AN ANOMALOUS GAUGE THEORY

1989 ◽  
Vol 04 (08) ◽  
pp. 775-782 ◽  
Author(s):  
SHOGO MIYAKE ◽  
KEN-ICHI SHIZUYA
Keyword(s):  
Gauge Theory ◽  
Schwinger Model ◽  
Anomalous Form ◽  
Symmetric Formulation

We investigate the conventional (anomalous) form of the chiral Schwinger model via its gauge-symmetric formulation and point out some unusual (noncanonical) features of it. We clarify their origin and discuss the problem of fermion confinement in this model.

REALIZATION OF THE FADDEEVIAN REGULARIZATION IN AN ANOMALOUS GAUGE THEORY

1993 ◽  
Vol 08 (37) ◽  
pp. 3497-3505
Author(s):  
YONG-WAN KIM ◽  
YOUNG-JAI PARK ◽  
KEE YONG KIM ◽  
YONGDUK KIM ◽  
WON-TAE KIM
Keyword(s):  
Gauge Theory ◽  
Hamiltonian Formulation ◽  
Generalized Model ◽  
Schwinger Model ◽  
Fixed Model

We analyze the minimal chiral Schwinger model with the Wess-Zumino action in the Hamiltonian formulation and show that Mitra’s “Faddeevian regularization” originates in the matter gauge-fixed model in the case of a regularization ambiguity with a=2. Furthermore, we obtain the generalized model which satisfies the Faddeevian regularization for a≥1.

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 Lattice gauge theory for the Haldane conjecture and central-branch Wilson fermion

2020 ◽  
Vol 2020 (3) ◽  
Author(s):  
Tatsuhiro Misumi ◽  
Yuya Tanizaki
Keyword(s):  
Gauge Theory ◽  
Lattice Gauge Theory ◽  
Fine Tuning ◽  
Lattice Rotation ◽  
Dirac Fermions ◽  
Wilson Fermion ◽  
Schwinger Model ◽  
Lattice Gauge ◽  
Sign Problem ◽  
The Continuum

Abstract We develop a $(1+1)$D lattice $U(1)$ gauge theory in order to define the two-flavor massless Schwinger model, and discuss its connection with the Haldane conjecture. We propose to use the central-branch Wilson fermion, which is defined by relating the mass, $m$, and the Wilson parameter, $r$, by $m+2r=0$. This setup gives two massless Dirac fermions in the continuum limit, and it turns out that no fine-tuning of $m$ is required because the extra $U(1)$ symmetry at the central branch, $U(1)_{\overline{V}}$, prohibits additive mass renormalization. Moreover, we show that the Dirac determinant is positive semi-definite and this formulation is free from the sign problem, so a Monte Carlo simulation of the path integral is possible. By identifying the symmetry at low energy, we show that this lattice model has a mixed ’t Hooft anomaly between $U(1)_{\overline{V}}$, lattice translation, and lattice rotation. We discuss its relation to the anomaly of half-integer anti-ferromagnetic spin chains, so our lattice gauge theory is suitable for numerical simulation of the Haldane conjecture. Furthermore, it gives a new and strict understanding on the parity-broken phase (Aoki phase) of the $2$D Wilson fermion.

scholarly journals Features of a 2d gauge theory with vanishing chiral condensate

2014 ◽  
Vol 25 (10) ◽  
pp. 1450051 ◽  
Author(s):  
David Landa-Marbán ◽  
Wolfgang Bietenholz ◽  
Ivan Hip
Keyword(s):  
Gauge Theory ◽  
Anomalous Dimension ◽  
Recent Literature ◽  
Chiral Limit ◽  
Numerical Data ◽  
Chiral Condensate ◽  
Fermionic Model ◽  
Schwinger Model ◽  
Lattice Fermions

The Schwinger model with Nf ≥ 2 flavors is a simple example for a fermionic model with zero chiral condensate Σ (in the chiral limit). We consider numerical data for two light flavors, based on simulations with dynamical chiral lattice fermions. We test properties and predictions that were put forward in the recent literature for models with Σ = 0, which include IR conformal theories. In particular, we probe the decorrelation of low lying Dirac eigenvalues, and we discuss the mass anomalous dimension and its IR extrapolation. Here, we encounter subtleties, which may urge caution with analogous efforts in other models, such as multi-flavor QCD.

A LATTICE GLOBAL CHIRAL INVARIANT REGULARIZATION OF THE CHIRAL SCHWINGER MODEL

1990 ◽  
Vol 05 (04) ◽  
pp. 275-280 ◽  
Author(s):  
J.L. ALONSO ◽  
J.-L. CORTÈS ◽  
E. RIVAS ◽  
Ph. BOVCAUD
Keyword(s):  
Gauge Theory ◽  
Regularization Procedure ◽  
Schwinger Model ◽  
Chiral Invariance ◽  
Invariant Regularization

Working à la Wilson it is not possible to regularize a Chiral Gauge Theory maintaining the global chiral invariance. We propose a new Lattice fermionic regularization procedure preserving, besides the global chiral invariance, all the symmetries the Wilson method preserves. We apply this proposal to the Chiral Schwinger Model.

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.

COUPLED CLUSTER CALCULATIONS OF THE SCHWINGER MODEL IN HAMILTONIAN LATTICE GAUGE THEORY

2003 ◽  
Vol 17 (28) ◽  
pp. 5393-5396 ◽  
Author(s):  
REUBEN MCDONALD ◽  
NIELS R. WALET
Keyword(s):  
Gauge Theory ◽  
Ground State ◽  
Quantum Electrodynamics ◽  
Lattice Gauge Theory ◽  
Cluster Method ◽  
Coupled Cluster ◽  
Fermion Mass ◽  
Schwinger Model ◽  
Hamiltonian Lattice ◽  
Spatial Lattice

The Schwinger Model, or quantum electrodynamics in 1+1 dimensions is a simple, yet non-trivial gauge theory. We investigate the Hamiltonian form of the Schwinger model defined of a spatial lattice with massive staggered fermions using the normal coupled cluster method (NCCM). We concentrate on the ground state of the model, studying the ground state energy as a function of coupling and fermion mass.

CONSISTENT QUANTIZATION OF A CHIRAL GAUGE THEORY IN FOUR DIMENSIONS

1989 ◽  
Vol 04 (27) ◽  
pp. 2675-2683 ◽  
Author(s):  
SHOGO MIYAKE ◽  
KEN-ICHI SHIZUYA
Keyword(s):  
Gauge Theory ◽  
Gauge Symmetry ◽  
Gauge Field ◽  
Current Algebra ◽  
Gauge Theories ◽  
Present Theory ◽  
Particle Spectrum ◽  
Four Dimensions ◽  
Symmetric Formulation

Using a gauge-symmetric formulation of anomalous gauge theories, we study the consistency and symmetry contents of a chiral gauge theory in four dimensions. The gauge symmetry, restored by the inclusion of the Wess-Zumino term, is spontaneously broken and the gauge field acquires a mass. Symmetry arguments are used to determine the particle spectrum and the current algebra of the model. Our analysis indicates that, apart from a question of renormalizability, the present theory is a consistent gauge theory.

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