scholarly journals Nonperturbative quantization of the electroweak model’s electrodynamic sector

2015 ◽  
Vol 91 (8) ◽  
Author(s):  
M. P. Fry
Keyword(s):  
Nonperturbative Quantization

scholarly journals Modified gravity from the nonperturbative quantization of a metric

2015 ◽  
Vol 75 (4) ◽  
Author(s):  
Vladimir Dzhunushaliev ◽  
Vladimir Folomeev ◽  
Burkhard Kleihaus ◽  
Jutta Kunz
Keyword(s):  
Modified Gravity ◽  
Nonperturbative Quantization

scholarly journals NONPERTURBATIVE QUANTIZATION OF PHANTOM AND GHOST THEORIES: RELATING DEFINITE AND INDEFINITE REPRESENTATIONS

2007 ◽  
Vol 22 (14n15) ◽  
pp. 2563-2608 ◽  
Author(s):  
ANDRÉ VAN TONDER ◽  
MIQUEL DORCA
Keyword(s):  
Path Integral ◽  
Degrees Of Freedom ◽  
Ad Hoc ◽  
Inner Product ◽  
Product Spaces ◽  
Indefinite Inner Product ◽  
Inner Product Spaces ◽  
Physical Information ◽  
Definition Of ◽  
Nonperturbative Quantization

We investigate the nonperturbative quantization of phantom and ghost degrees of freedom by relating their representations in definite and indefinite inner product spaces. For a large class of potentials, we argue that the same physical information can be extracted from either representation. We provide a definition of the path integral for these theories, even in cases where the integrand may be exponentially unbounded, thereby removing some previous obstacles to their nonperturbative study. We apply our results to the study of ghost fields of Pauli–Villars and Lee–Wick type, and we show in the context of a toy model how to derive, from an exact nonperturbative path integral calculation, previously ad hoc prescriptions for Feynman diagram contour integrals in the presence of complex energies. We point out that the pole prescriptions obtained in ghost theories are opposite to what would have been expected if one had added conventional i∊ convergence factors in the path integral.

scholarly journals Cosmological constant and Euclidean space from nonperturbative quantum torsion

2014 ◽  
Vol 12 (01) ◽  
pp. 1550008
Author(s):  
Vladimir Dzhunushaliev
Keyword(s):  
Cosmological Constant ◽  
Vector Fields ◽  
Affine Connection ◽  
Classical Field ◽  
Christoffel Symbols ◽  
Scalar And Vector Fields ◽  
Quantization Of Gravity ◽  
Classical Part ◽  
Infinite Set ◽  
Nonperturbative Quantization

Heisenberg's nonperturbative quantization technique is applied to the nonperturbative quantization of gravity. An infinite set of equations for all Green's functions is obtained. An approximation is considered where: (a) the metric remains as a classical field; (b) the affine connection can be decomposed into classical and quantum parts; (c) the classical part of the affine connection is the Christoffel symbols; (d) the quantum part is the torsion. Using a scalar and vector fields approximation it is shown that nonperturbative quantum effects give rise to a cosmological constant and an Euclidean solution.

scholarly journals Mass Gap in Nonperturbative Quantization à La Heisenberg

Universe ◽  
2019 ◽  
Vol 5 (2) ◽  
pp. 50
Author(s):  
Vladimir Dzhunushaliev ◽  
Vladimir Folomeev
Keyword(s):  
Energy Spectrum ◽  
Approximate Method ◽  
Quark Gluon Plasma ◽  
Degrees Of Freedom ◽  
Finite Energy ◽  
Gluon Plasma ◽  
Spherically Symmetric ◽  
Mass Gap ◽  
Infinite Set ◽  
Nonperturbative Quantization

The approximate method of solving nonperturbative Dyson-Schwinger equations by cutting off this infinite set of equations to three equations is considered. The gauge noninvariant decomposition of SU(3) degrees of freedom into SU(2) × U(1) and SU(3)/(SU(2) × U(1)) degrees of freedom is used. SU(2) × U(1) degrees of freedom have nonzero quantum average, and SU(3)/(SU(2) × U(1)) have zero quantum average. To close these equations, some approximations are employed. Regular spherically symmetric finite energy solutions of these equations are obtained. Energy spectrum of these solutions is studied. The presence of a mass gap is shown. The obtained solutions describe quasi-particles in a quark-gluon plasma.

scholarly journals Nonperturbative Quantization Approach for QED on the Hopf Bundle

Universe ◽  
2021 ◽  
Vol 7 (3) ◽  
pp. 65
Author(s):  
Vladimir Dzhunushaliev ◽  
Vladimir Folomeev
Keyword(s):  
Dirac Equation ◽  
Three Dimensional ◽  
Quantum States ◽  
Classical Solutions ◽  
Dimensional Sphere ◽  
Operator Equations ◽  
Maxwell Fields ◽  
Discrete Spectra ◽  
Infinite Set ◽  
Nonperturbative Quantization

We consider the Dirac equation and Maxwell’s electrodynamics in R×S3 spacetime, where a three-dimensional sphere is the Hopf bundle S3→S2. In both cases, discrete spectra of classical solutions are obtained. Based on the solutions obtained, the quantization of free, noninteracting Dirac and Maxwell fields is carried out. The method of nonperturbative quantization of interacting Dirac and Maxwell fields is suggested. The corresponding operator equations and the infinite set of the Schwinger–Dyson equations for Green’s functions is written down. We write a simplified set of equations describing some physical situations to illustrate the suggested scheme of nonperturbative quantization. Additionally, we discuss the properties of quantum states and operators of interacting fields.

scholarly journals STRONG COUPLING LIMITS AND QUANTUM ISOMORPHISMS OF THE GAUGED THIRRING MODEL

2011 ◽  
Vol 26 (09) ◽  
pp. 1545-1560 ◽  
Author(s):  
R. BUFALO ◽  
R. CASANA ◽  
B. M. PIMENTEL
Keyword(s):  
Strong Coupling ◽  
Green's Functions ◽  
Green’S Functions ◽  
Transition Amplitude ◽  
Constrained Systems ◽  
Thirring Model ◽  
Integral Approach ◽  
Constraint Structure ◽  
Dirac's Formalism ◽  
Nonperturbative Quantization

We have studied the quantum equivalence in the respective strong coupling limits of the bidimensional gauged Thirring model with both Schwinger and Thirring models. It is achieved following a nonperturbative quantization of the gauged Thirring model into the path-integral approach. First, we have established the constraint structure via the Dirac's formalism for constrained systems and defined the correct vacuum–vacuum transition amplitude by using the Faddeev–Senjanovic method. Next, we have computed exactly the relevant Green's functions and shown the Ward–Takahashi identities. Afterwards, we have established the quantum isomorphisms between gauged Thirring model and both Schwinger and Thirring models by analyzing the respective Green's functions in the strong coupling limits, respectively. A special attention is necessary to establish the quantum isomorphism between the gauged Thirring model and the Thirring model.

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