ON EXACT HYPERGEOMETRIC SOLUTIONS OF CERTAIN SOLITON-LIKE EQUATIONS

2010 ◽  
Vol 24 (23) ◽  
pp. 4509-4519
Author(s):  
V. F. TARASOV
Keyword(s):  
Hypergeometric Functions ◽  
Evolution Equations ◽  
Boussinesq Equation ◽  
Dimensional Space ◽  
Quantum Field ◽  
Soliton Theory ◽  
Functional Relations ◽  
Dimensional Space Time ◽  
Model Equations ◽  
Hypergeometric Solutions

It is shown that certain nonlinear wave evolution equations in (1+1)-dimensional space-time in the soliton theory: sine-Gordon (SG), sinh-Gordon (ShG), the nonlinear Schrödinger equation (NLS), the φ4 equation in quantum field theory, the Burgers diffusion equation (Brg) and the Huxley equation (Hsl) in biophysics, the Boussinesq equation (Bsq), can be solved in terms of hypergeometric functions of pFq-type. Such approach allows to establish the connection between "model" equations and simple functional relations (in the form of diagrams) of these functions; the latter gives the possibility to consider a number of "inverse problems" in the soliton theory in a new way and to get new "models" of solitary waves.

scholarly journals Scenario for the renormalization in the 4D Yang–Mills theory

2016 ◽  
Vol 31 (01) ◽  
pp. 1630001 ◽  
Author(s):  
L. D. Faddeev
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Dimensional Space ◽  
Background Field ◽  
Space Time ◽  
Quantum Field ◽  
Yang Mills ◽  
Dimensional Space Time ◽  
Field Formalism

The renormalizability of the Yang–Mills quantum field theory in four-dimensional space–time is discussed in the background field formalism.

On Borchers class of Markoff fields

1974 ◽  
Vol 76 (2) ◽  
pp. 457-463 ◽  
Author(s):  
W. Karwowski
Keyword(s):  
Minkowski Space ◽  
Dimensional Space ◽  
Probabilistic Methods ◽  
Quantum Field ◽  
Two Dimensional ◽  
Higher Dimension ◽  
Dimensional Space Time ◽  
Wightman Fields ◽  
Wightman Axioms ◽  
Space Approach

The possibility of constructing a quantum field theory by means of fields on Euclidean space is based on works by Schwinger and Symanzik (1). Probabilistic methods were used and Nelson has shown (2) that from so-called ‘Markoff fields’ one can construct Wightman fields. This idea turned out to be unusually fruitful as it made available the statistical mechanic's techniques for consideration of quantumfield theory problems. See for example (7). However as in the Minkowski space approach, the only two-dimensional space-time nontrivial models have been proved to fulfil all Wightman axioms. Since the problem for higher dimension theories is still open and extremely difficult, it is useful to have at least some criterion which allows us to eliminate certain procedures as leading to trivial theories. One such criterion existing in the Minkowski space approach is described by a notion of Borchers class (5).

scholarly journals Quantum control using quantum memory

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Mathieu Roget ◽  
Basile Herzog ◽  
Giuseppe Di Molfetta
Keyword(s):  
Quantum Control ◽  
Dimensional Space ◽  
Quantum Memory ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Medium Term ◽  
Initial State ◽  
Quantum Devices ◽  
Dimensional Space Time ◽  
Time Grid

AbstractWe propose a new quantum numerical scheme to control the dynamics of a quantum walker in a two dimensional space–time grid. More specifically, we show how, introducing a quantum memory for each of the spatial grid, this result can be achieved simply by acting on the initial state of the whole system, and therefore can be exactly controlled once for all. As example we prove analytically how to encode in the initial state any arbitrary walker’s mean trajectory and variance. This brings significantly closer the possibility of implementing dynamically interesting physics models on medium term quantum devices, and introduces a new direction in simulating aspects of quantum field theories (QFTs), notably on curved manifold.

scholarly journals PRIME NUMBERS, QUANTUM FIELD THEORY AND THE GOLDBACH CONJECTURE

2012 ◽  
Vol 27 (23) ◽  
pp. 1250136 ◽  
Author(s):  
MIGUEL-ANGEL SANCHIS-LOZANO ◽  
J. FERNANDO BARBERO G. ◽  
JOSÉ NAVARRO-SALAS
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Fock Space ◽  
Dimensional Space ◽  
Canonical Quantization ◽  
Prime Numbers ◽  
Large Integer ◽  
Quantum Field ◽  
Dimensional Space Time ◽  
Prime Fields

Motivated by the Goldbach conjecture in number theory and the Abelian bosonization mechanism on a cylindrical two-dimensional space–time, we study the reconstruction of a real scalar field as a product of two real fermion (so-called prime) fields whose Fourier expansion exclusively contains prime modes. We undertake the canonical quantization of such prime fields and construct the corresponding Fock space by introducing creation operators [Formula: see text] — labeled by prime numbers p — acting on the vacuum. The analysis of our model, based on the standard rules of quantum field theory and the assumption of the Riemann hypothesis, allows us to prove that the theory is not renormalizable. We also comment on the potential consequences of this result concerning the validity or breakdown of the Goldbach conjecture for large integer numbers.

scholarly journals Solitary Wave Solutions for Some Fractional Evolution Equations via New Kudryashov Approach

2021 ◽  
Vol 68 (1 Jan-Feb) ◽  
Author(s):  
Serife Muge Ege
Keyword(s):  
Solitary Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Dimensional Space ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Kudryashov Method ◽  
Dimensional Space Time ◽  
Fifth Order ◽  
Physical Phenomena

In this work, we construct solitary wave solutions of a nonlinear evolution equation in the physical phenomena of waves;namely the time-fractional fifth-order Sawada-Kotera equation and the (4+1)-dimensional space-time fractional Fokas equation by Kudryashov method with a new function. As a result, new types of exact analytical solutions are obtained. Here the fractional derivative is described in beta sense.  

scholarly journals String solutions in AdS3 × S3 × S3 × S1 with B-field

2017 ◽  
Vol 32 (01) ◽  
pp. 1750007
Author(s):  
Plamen Bozhilov
Keyword(s):  
Hypergeometric Functions ◽  
Dimensional Space ◽  
Space Time ◽  
Elliptic Integrals ◽  
Conserved Charges ◽  
Text Field ◽  
Angular Momenta ◽  
Dimensional Space Time ◽  
Incomplete Elliptic Integrals

We consider strings living in [Formula: see text] with nonzero [Formula: see text]-field. By using specific ansatz for the string embedding, we obtain a class of solutions corresponding to strings moving in the whole ten-dimensional space–time. For the [Formula: see text] subspace, these solutions are given in terms of incomplete elliptic integrals. For the two three-spheres, they are expressed in terms of Lauricella hypergeometric functions of many variables. The conserved charges, i.e. the string energy, spin and angular momenta, are also found.

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