scholarly journals Extrapolating the precision of the hypergeometric resummation to strong couplings with application to the 𝒫𝒯-symmetric iϕ3 field theory

2020 ◽  
Vol 35 (08) ◽  
pp. 2050041 ◽  
Author(s):  
Abouzeid M. Shalaby
Keyword(s):  
Field Theory ◽  
Hypergeometric Function ◽  
State Energy ◽  
Strong Coupling Expansion ◽  
Perturbation Series ◽  
Three Dimensions ◽  
Symmetric Model ◽  
Large Coupling ◽  
First Order ◽  
Exact Calculations

In Phys. Rev. Lett. 115, 143001 (2015), H. Mera et al. developed a new simple but precise hypergeometric resummation technique. In this work, we suggest to obtain half of the parameters of the hypergeometric function from the strong-coupling expansion of the physical quantity. Since these parameters are taking now their exact values they can improve the precision of the technique for the whole range of the coupling values. The second order approximant [Formula: see text] of the algorithm is applied to resum the perturbation series of the ground state energy of the [Formula: see text]-symmetric [Formula: see text] field theory. It gives accurate results compared to exact calculations from the literature specially for very large coupling values. The [Formula: see text]-symmetry breaking of the Yang–Lee model has been investigated where third, fourth and fifth orders were able to get very accurate results when compared to other resummation methods involving [Formula: see text] orders. The critical exponent [Formula: see text] of the [Formula: see text]-symmetric model in three dimensions has been precisely obtained using only first order of perturbation series as input. The algorithm can be extended easily to accommodate any order of perturbation series in using the generalized hypergeometric function [Formula: see text] as it shares the same analytic properties with [Formula: see text].

Perturbation theory and the local compressibility approximation in classical statistical mechanics

1968 ◽  
Vol 46 (15) ◽  
pp. 1725-1727 ◽  
Author(s):  
W. R. Smith ◽  
D. Henderson ◽  
J. A. Barker
Keyword(s):  
Perturbation Theory ◽  
Statistical Mechanics ◽  
Order Term ◽  
Second Order ◽  
Three Dimensions ◽  
First Order ◽  
Classical Statistical Mechanics ◽  
Square Well ◽  
Exact Calculations

The integrals which appear in the first-order term and the local compressibility approximation to the second-order term in the Barker–Henderson perturbation theory of fluids are evaluated analytically for the square-well potential in one and three dimensions and are compared with exact calculations.

scholarly journals Is there supersymmetric Lee–Yang fixed point in three dimensions?

2021 ◽  
pp. 2150176
Author(s):  
Yu Nakayama
Keyword(s):  
Field Theory ◽  
Phase Transition ◽  
Fixed Point ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Natural Question ◽  
First Order ◽  
Conformal Bootstrap ◽  
First Order Transition

The supersymmetric Lee–Yang model is arguably the simplest interacting supersymmetric field theory in two dimensions, albeit nonunitary. A natural question is if there is an analogue of supersymmetric Lee–Yang fixed point in higher dimensions. The absence of any [Formula: see text] symmetry (except for fermion numbers) makes it impossible to approach it by using perturbative [Formula: see text] expansions. We find that the truncated conformal bootstrap suggests that candidate fixed points obtained by the dimensional continuation from two dimensions annihilate below three dimensions, implying that there is no supersymmetric Lee–Yang fixed point in three dimensions. We conjecture that the corresponding phase transition, if any, will be the first-order transition.

QLB for Quantum Many-Body and Quantum Field Theory

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Quantum Computing ◽  
Single Particle ◽  
Body Problem ◽  
Three Dimensions ◽  
Quantum Field ◽  
Many Body ◽  
Quantum Particles

Chapter 32 expounded the basic theory of quantum LB for the case of relativistic and non-relativistic wavefunctions, namely single-particle quantum mechanics. This chapter goes on to cover extensions of the quantum LB formalism to the overly challenging arena of quantum many-body problems and quantum field theory, along with an appraisal of prospective quantum computing implementations. Solving the single particle Schrodinger, or Dirac, equation in three dimensions is a computationally demanding task. This task, however, pales in front of the ordeal of solving the Schrodinger equation for the quantum many-body problem, namely a collection of many quantum particles, typically nuclei and electrons in a given atom or molecule.

scholarly journals Dissipation in the effective field theory for hydrodynamics: First-order effects

2013 ◽  
Vol 88 (10) ◽  
Author(s):  
Solomon Endlich ◽  
Alberto Nicolis ◽  
Rafael A. Porto ◽  
Junpu Wang
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Effective Field ◽  
Order Effects ◽  
First Order

scholarly journals Cosmological phase transitions: is effective field theory just a toy?

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Marieke Postma ◽  
Graham White
Keyword(s):  
Field Theory ◽  
Phase Transition ◽  
Phase Transitions ◽  
Effective Field Theory ◽  
New Physics ◽  
Effective Field ◽  
Tree Level ◽  
Dark Sector ◽  
First Order ◽  
First Order Phase

Abstract To obtain a first order phase transition requires large new physics corrections to the Standard Model (SM) Higgs potential. This implies that the scale of new physics is relatively low, raising the question whether an effective field theory (EFT) description can be used to analyse the phase transition in a (nearly) model-independent way. We show analytically and numerically that first order phase transitions in perturbative extensions of the SM cannot be described by the SM-EFT. The exception are Higgs-singlet extension with tree-level matching; but even in this case the SM-EFT can only capture part of the full parameter space, and if truncated at dim-6 operators, the description is at most qualitative. We also comment on the applicability of EFT techniques to dark sector phase transitions.

PATH-INTEGRAL APPROACH FOR ELECTRON–PHONON INTERACTION EFFECTS IN HARMONIC QUANTUM DOTS

1996 ◽  
Vol 10 (22) ◽  
pp. 2781-2796 ◽  
Author(s):  
SOMA MUKHOPADHYAY ◽  
ASHOK CHATTERJEE
Keyword(s):  
Quantum Dots ◽  
Path Integral ◽  
State Energy ◽  
Coupling Parameter ◽  
Three Dimensions ◽  
Integral Approach ◽  
Phonon Coupling ◽  
Electron Phonon Interaction ◽  
Electron Phonon Coupling ◽  
Parabolic Confinement

We use the Feynman–Haken path-integral formalism to obtain the polaronic correction to the ground state energy of an electron in a polar semiconductor quantum dot with parabolic confinement in both two and three dimensions. We perform calculations for the entire range of the electron–phonon coupling parameter and for arbitrary confinement length. We apply our results to several semiconductor quantum dots and show that the polaronic effect in some of these dots can be considerably large if the dot sizes are made smaller than a few nanometers.

scholarly journals Quantum Field Theory over $\mathbb{F}_q$

10.37236/589 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Oliver Schnetz
Keyword(s):  
Field Theory ◽  
Perturbation Series ◽  
The Other ◽  
Field Theories ◽  
Roots Of Unity ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Feynman Rules ◽  
Graph Hypersurfaces ◽  
Prime 2

We consider the number $\bar N(q)$ of points in the projective complement of graph hypersurfaces over $\mathbb{F}_q$ and show that the smallest graphs with non-polynomial $\bar N(q)$ have 14 edges. We give six examples which fall into two classes. One class has an exceptional prime 2 whereas in the other class $\bar N(q)$ depends on the number of cube roots of unity in $\mathbb{F}_q$. At graphs with 16 edges we find examples where $\bar N(q)$ is given by a polynomial in $q$ plus $q^2$ times the number of points in the projective complement of a singular K3 in $\mathbb{P}^3$. In the second part of the paper we show that applying momentum space Feynman-rules over $\mathbb{F}_q$ lets the perturbation series terminate for renormalizable and non-renormalizable bosonic quantum field theories.

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