Feynman integrals ofp-adic argument in the momentum space. II. Explicit expressions

1995 ◽  
Vol 104 (3) ◽  
pp. 1061-1077 ◽  
Author(s):  
É. Yu. Lerner
Keyword(s):  
Momentum Space ◽  
Feynman Integrals ◽  
Explicit Expressions

scholarly journals Yangian bootstrap for massive Feynman integrals

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Florian Loebbert ◽  
Julian Miczajka ◽  
Dennis Müller ◽  
Hagen Münkler
Keyword(s):  
Momentum Space ◽  
Conformal Symmetry ◽  
Feynman Integrals ◽  
Series Representations ◽  
Yangian Symmetry

We extend the study of the recently discovered Yangian symmetry of massive Feynman integrals and its relation to massive momentum space conformal symmetry. After proving the symmetry statements in detail at one and two loop orders, we employ the conformal and Yangian constraints to bootstrap various one-loop examples of massive Feynman integrals. In particular, we explore the interplay between Yangian symmetry and hypergeometric expressions of the considered integrals. Based on these examples we conjecture single series representations for all dual conformal one-loop integrals in D spacetime dimensions with generic massive propagators.

scholarly journals Reduction of Feynman integrals in the parametric representation III: integrals with cuts

2020 ◽  
Vol 80 (12) ◽  
Author(s):  
Wen Chen
Keyword(s):  
Phase Space ◽  
Differential Equations ◽  
Momentum Space ◽  
Theta Functions ◽  
Parametric Representation ◽  
Systematic Method ◽  
Integration By Parts ◽  
Feynman Integrals

AbstractPhase space cuts are implemented by inserting Heaviside theta functions in the integrands of momentum-space Feynman integrals. By directly parametrizing theta functions and constructing integration-by-parts (IBP) identities in the parametric representation, we provide a systematic method to reduce integrals with cuts. Since the IBP method is available, it becomes possible to evaluate integrals with cuts by constructing and solving differential equations.

Classical and generalized of a mixed problem– solutions for a non-homogeneous wave equation

2019 ◽  
Vol 484 (1) ◽  
pp. 18-20
Author(s):  
A. P. Khromov ◽  
V. V. Kornev
Keyword(s):  
Wave Equation ◽  
Fourier Series ◽  
Mixed Problem ◽  
Homogeneous Equation ◽  
Generalized Solution ◽  
Problem Solution ◽  
Homogeneous Wave ◽  
Homogeneous Wave Equation ◽  
Explicit Expressions

This study follows A.N. Krylov’s recommendations on accelerating the convergence of the Fourier series, to obtain explicit expressions of the classical mixed problem–solution for a non-homogeneous equation and explicit expressions of the generalized solution in the case of arbitrary summable functions q(x), ϕ(x), y(x), f(x, t).

scholarly journals Application of a momentum-space semi-locally regularized chiral potential to selected disintegration processes

2021 ◽  
Vol 103 (2) ◽  
Author(s):  
V. Urbanevych ◽  
R. Skibiński ◽  
H. Witała ◽  
J. Golak ◽  
K. Topolnicki ◽  
...  
Keyword(s):  
Momentum Space ◽  
Chiral Potential

scholarly journals Minkowski box from Yangian bootstrap

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Luke Corcoran ◽  
Florian Loebbert ◽  
Julian Miczajka ◽  
Matthias Staudacher
Keyword(s):  
Minkowski Space ◽  
Wigner Function ◽  
Functional Form ◽  
A Priori ◽  
Alternative Methods ◽  
Feynman Integrals ◽  
The One

Abstract We extend the recently developed Yangian bootstrap for Feynman integrals to Minkowski space, focusing on the case of the one-loop box integral. The space of Yangian invariants is spanned by the Bloch-Wigner function and its discontinuities. Using only input from symmetries, we constrain the functional form of the box integral in all 64 kinematic regions up to twelve (out of a priori 256) undetermined constants. These need to be fixed by other means. We do this explicitly, employing two alternative methods. This results in a novel compact formula for the box integral valid in all kinematic regions of Minkowski space.

scholarly journals The Dirac Sea, T and C Symmetry Breaking, and the Spinor Vacuum of the Universe

Universe ◽  
2021 ◽  
Vol 7 (5) ◽  
pp. 124
Author(s):  
Vadim Monakhov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Symmetry Breaking ◽  
Momentum Space ◽  
Quantum Field ◽  
Conjugation Operator ◽  
Dirac Sea ◽  
Canonical Anticommutation Relations ◽  
The Universe ◽  
Dirac Conjugation

We have developed a quantum field theory of spinors based on the algebra of canonical anticommutation relations (CAR algebra) of Grassmann densities in the momentum space. We have proven the existence of two spinor vacua. Operators C and T transform the normal vacuum into an alternative one, which leads to the breaking of the C and T symmetries. The CPT is the real structure operator; it preserves the normal vacuum. We have proven that, in the theory of the Dirac Sea, the formula for the charge conjugation operator must contain an additional generalized Dirac conjugation operator.

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