scholarly journals Generalized version of chiral Schwinger model in terms of chiral bosonization

2021 ◽  
Vol 81 (3) ◽  
Author(s):  
Safia Yasmin
Keyword(s):  
Degrees Of Freedom ◽  
Lorentz Invariance ◽  
Axial Vector ◽  
Hamiltonian Formalism ◽  
Generalized Model ◽  
Schwinger Model ◽  
Vector Interaction ◽  
Poincaré Algebra

AbstractThe $$(1+1)$$ ( 1 + 1 ) dimensional generalized model where vector and axial vector interaction get mixed up with different strength is considered. Imposing a chiral constraint, the model can be expressed in terms of chiral boson. Then the theoretical spectra of this model has been determined in both the Lagrangian and Hamiltonian formalism. It is found that the massless degrees of freedom disappears from the spectra and the photon acquires mass as well. Imposition of chiral constraint brings a disaster so far as Lorentz invariance is concerned. An attempt has been made here to show the physical Lorentz invariance explicitly using Poincaré algebra.

Degrees of freedom and problems in f(T) gravity

2018 ◽  
Vol 15 (supp01) ◽  
pp. 1850139 ◽  
Author(s):  
Yen Chin Ong
Keyword(s):  
Degrees Of Freedom ◽  
Lorentz Invariance ◽  
Modified Theories Of Gravity ◽  
Recent Effort ◽  
Original Formulation ◽  
Actual Number ◽  
Specific Choice ◽  
Superluminal Propagation ◽  
Theories Of Gravity ◽  
Local Lorentz Invariance

Torsion-based modified theories of gravity, such as [Formula: see text] gravity, are arguably one of the very few “true” modified gravities based on well-defined geometric structures. However, the original formulation explicitly works in a specific choice of frame, which has led to considerable amount of confusion in the literature about these theories breaking local Lorentz invariance. Pathological properties such as superluminal propagation and the lack of well-posedness of Cauchy problem were found to plague [Formula: see text] gravity. Recent effort to “covariantize” [Formula: see text] gravity has, however, renewed interests in this subject. In this proceeding paper, we review and discuss issues concerning the actual number of degrees of freedom in [Formula: see text] gravity, and how this might relate to the aforementioned pathologies.

scholarly journals Hamiltonian formalism for nonlocal gravity models

2022 ◽  
Author(s):  
Pawan Joshi ◽  
Utkarsh Kumar ◽  
Sukanta Panda
Keyword(s):  
Ricci Tensor ◽  
Degrees Of Freedom ◽  
Hamiltonian Formalism ◽  
Riemann Tensor ◽  
Ricci Scalar ◽  
Gravity Models ◽  
Lagrangian Formalism ◽  
Acceleration Of The Universe ◽  
Nonlocal Action ◽  
The Universe

Nonlocal gravity models are constructed to explain the current acceleration of the universe. These models are inspired by the infrared correction appearing in Einstein–Hilbert action. Here, we develop the Hamiltonian formalism of a nonlocal model by considering only terms to quadratic order in Riemann tensor, Ricci tensor and Ricci scalar. We show how to count degrees of freedom using Hamiltonian formalism including Ricci tensor and Ricci scalar terms. In this model, we have also worked out with a choice of a nonlocal action which has only two degrees of freedom equivalent to GR. Finally, we find the existence of additional constraints in Hamiltonian required to remove the ghosts in our full action. We also compare our results with that of obtained using Lagrangian formalism.

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.

scholarly journals BARYONS AS THREE-FLAVOR SOLITONS

1996 ◽  
Vol 11 (14) ◽  
pp. 2419-2544 ◽  
Author(s):  
HERBERT WEIGEL
Keyword(s):  
Symmetry Breaking ◽  
Vector Meson ◽  
Degrees Of Freedom ◽  
Magnetic Moments ◽  
Axial Vector ◽  
Vector Current ◽  
Bound State ◽  
Axial Vector Current ◽  
Flavor Symmetry ◽  
Matrix Elements

The description of baryons as soliton solutions of effective meson theories for three-flavor (up, down and strange) degrees of freedom is reviewed and the phenomenological implications are illuminated. In the collective approach the soliton configuration is equipped with baryon quantum numbers by canonical quantization of the coordinates describing the flavor orientation. The baryon spectrum resulting from exact diagonalization of the collective Hamiltonian is discussed. The prediction of static properties, such as the baryon magnetic moments and the Cabibbo matrix elements for semileptonic hyperon decays, are explored with regard to the influence of flavor symmetry breaking. In particular, the role of strange degrees of freedom in the nucleon is investigated for both the vector and axial vector current matrix elements. The latter are discussed extensively within the context of the proton spin puzzle. The influence of flavor symmetry breaking on the shape of the soliton is examined, and observed to cause significant deviations from flavor-covariant predictions on the baryon magnetic moments. Short range effects are incorporated by a chirally invariant inclusion of vector meson fields. These extensions are necessary for properly describing the singlet axial vector current and the neutron–proton mass difference. The effects of the vector meson excitations on baryon properties are also considered. The bound state description of hyperons and its generalization to baryons containing a heavy quark are illustrated. In the case of the Skyrme model a comparison is made between the collective quantization scheme and the bound state approach. Finally, the Nambu–Jona-Lasinio model is employed to demonstrate that hyperons can be described as solitons in a microscopic theory of the quark flavor dynamics. This is explained for both the collective and the bound state approaches to strangeness.

scholarly journals Some Lessons from the Schwinger Model

1997 ◽  
Vol 12 (06) ◽  
pp. 1091-1099 ◽  
Author(s):  
Gary McCartor
Keyword(s):  
Boundary Conditions ◽  
Degrees Of Freedom ◽  
Chiral Condensate ◽  
Number Of Solutions ◽  
Different Boundary Conditions ◽  
Schwinger Model ◽  
The Way

I shall recall a number of solutions to the Schwinger model in different gauges, having different boundary conditions and using different quantization surfaces. I shall discuss various properties of these solutions emphasizing the degrees of freedom necessary to represent the solution, the way the operator products are defined and the effects these features have on the chiral condensate.

scholarly journals On the consistency of Lorentz invariance violation in QED induced by fermions in constant axial-vector background

2006 ◽  
Vol 639 (5) ◽  
pp. 586-590 ◽  
Author(s):  
J. Alfaro ◽  
A.A. Andrianov ◽  
M. Cambiaso ◽  
P. Giacconi ◽  
R. Soldati
Keyword(s):  
Lorentz Invariance ◽  
Axial Vector ◽  
Invariance Violation ◽  
Lorentz Invariance Violation

Generalized Hamiltonian dynamics

1958 ◽  
Vol 246 (1246) ◽  
pp. 326-332 ◽  
Keyword(s):  
Degrees Of Freedom ◽  
Hamiltonian Dynamics ◽  
Hamiltonian Formalism ◽  
Direct Solution ◽  
Independent Functions

The author’s procedure for passing from the Lagrangian to the Hamiltonian when the momenta are not independent functions of the velocities is put into a simpler and more practical form, the main results being obtained by a direct solution of the equations provided by the consistency requirements. It is shown how, under certain conditions, one can eliminate some of the degrees of freedom and so make a substantial simplification in the Hamiltonian formalism.

scholarly journals FERMIONS FROM PHOTONS: BOSONIZATION OF QED IN 2+1 DIMENSIONS

1994 ◽  
Vol 09 (27) ◽  
pp. 4669-4700 ◽  
Author(s):  
A. KOVNER ◽  
P.S. KURZEPA
Keyword(s):  
Perturbation Theory ◽  
Vector Potential ◽  
Energy Momentum Tensor ◽  
Lorentz Invariance ◽  
Hamiltonian Formalism ◽  
Momentum Tensor ◽  
Regularization Procedure ◽  
Local Polynomial ◽  
Definition Of ◽  
Chern Simons

We perform the complete bosonization of (2+1)-dimensional QED with one fermionic flavor in the Hamiltonian formalism. The Fermi operators are explicitly constructed in terms of the vector potential and the electric field. We carefully specify the regularization procedure involved in the definition of these operators, and calculate the fermionic bilinears and the energy-momentum tensor. The algebra of bilinears exhibits the Schwinger terms which also appear in perturbation theory. The bosonic Hamiltonian is a local, polynomial functional of Ai and Ei, and we check explicitly the Lorentz invariance of the resulting bosonic theory. Our construction is conceptually very similar to Mandelstam’s construction in 1+1 dimensions, and is dissimilar from the recent bosonization attempts in 2+1 dimensions, which hinge crucially on the presence of a Chern-Simons term.

scholarly journals Aspects of emergent symmetries

2016 ◽  
Vol 31 (10) ◽  
pp. 1630009 ◽  
Author(s):  
Pedro R. S. Gomes
Keyword(s):  
Field Theory ◽  
Statistical Mechanics ◽  
Degrees Of Freedom ◽  
Condensed Matter ◽  
Lorentz Invariance ◽  
Low Energy ◽  
Background Material

These are intended to be review notes on emergent symmetries, i.e. symmetries which manifest themselves in specific sectors of energy in many systems. The emphasis is on the physical aspects rather than computation methods. We include some background material and go through more recent problems in field theory, statistical mechanics and condensed matter. These problems illustrate how some important symmetries, such as Lorentz invariance and supersymmetry, usually believed to be fundamental, can arise naturally in low-energy regimes of systems involving a large number of degrees of freedom. The aim is to discuss how these examples could help us to face other complex and fundamental problems.

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