scholarly journals Symmetry factors of Feynman diagrams and the homological perturbation lemma

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Christian Saemann ◽  
Emmanouil Sfinarolakis
Keyword(s):  
Scalar Field ◽  
Scattering Amplitudes ◽  
General Formula ◽  
Feynman Diagram ◽  
Direct Proof ◽  
Feynman Diagrams ◽  
Field Theories ◽  
Polynomial Potential ◽  
Symmetry Factor ◽  
Homological Perturbation

Abstract We discuss the symmetry factors of Feynman diagrams of scalar field theories with polynomial potential. After giving a concise general formula for them, we present an elementary and direct proof that when computing scattering amplitudes using the homological perturbation lemma, each contributing Feynman diagram is indeed included with the correct symmetry factor.

scholarly journals A general expression for symmetry factors of Feynman diagrams

2002 ◽  
Vol 80 (8) ◽  
pp. 847-854 ◽  
Author(s):  
C D Palmer ◽  
M E Carrington
Keyword(s):  
General Expression ◽  
Feynman Diagram ◽  
Simple Formula ◽  
Feynman Diagrams ◽  
Scalar Theory ◽  
Symmetry Factor

The calculation of the symmetry factor corresponding to a given Feynman diagram is well known to be a tedious problem. We have derived a simple formula for these symmetry factors. Our formula works for any diagram in scalar theory (ϕ3 and ϕ4 interactions), spinor QED, scalar QED, or QCD. PACS Nos.: 11.10-z, 11.15-q, 11.15Bt

scholarly journals GEOMETRICALLY RELATING MOMENTUM CUT-OFF AND DIMENSIONAL REGULARIZATION

2012 ◽  
Vol 10 (02) ◽  
pp. 1250081 ◽  
Author(s):  
SUSAMA AGARWALA
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Hopf Algebras ◽  
Dimensional Regularization ◽  
Mass Scale ◽  
Feynman Diagrams ◽  
Field Theories ◽  
Coupling Constant ◽  
Regularization Scheme ◽  
Β Function

The β function for a scalar field theory describes the dependence of the coupling constant on the renormalization mass scale. This dependence is affected by the choice of regularization scheme. I explicitly relate the β functions of momentum cut-off regularization and dimensional regularization on scalar field theories by a gauge transformation using the Hopf algebras of the Feynman diagrams of the theories.

scholarly journals Extremal effective field theories

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Simon Caron-Huot ◽  
Vincent Van Duong
Keyword(s):  
Scalar Field ◽  
Scattering Amplitudes ◽  
Effective Field Theories ◽  
Convex Hull ◽  
Short Distance ◽  
Large Fraction ◽  
Effective Field ◽  
Field Theories ◽  
Long Distance ◽  
Distance Effects

Abstract Effective field theories (EFT) parameterize the long-distance effects of short-distance dynamics whose details may or may not be known. Previous work showed that EFT coefficients must obey certain positivity constraints if causality and unitarity are satisfied at all scales. We explore those constraints from the perspective of 2 → 2 scattering amplitudes of a light real scalar field, using semi-definite programming to carve out the space of allowed EFT coefficients for a given mass threshold M. We point out that all EFT parameters are bounded both below and above, effectively showing that dimensional analysis scaling is a consequence of causality. This includes the coefficients of s2 + t2 + u2 and stu type interactions. We present simple 2 → 2 extremal amplitudes which realize, or “rule in”, kinks in coefficient space and whose convex hull span a large fraction of the allowed space.

scholarly journals Feynman diagrams and rooted maps

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 149-167 ◽  
Author(s):  
Andrea Prunotto ◽  
Wanda Maria Alberico ◽  
Piotr Czerski
Keyword(s):  
Single Particle ◽  
Feynman Diagram ◽  
Feynman Diagrams ◽  
Topological Properties ◽  
Many Body ◽  
Perturbative Order ◽  
Original Definition ◽  
Many Body Systems ◽  
Definition Of ◽  
Particle Propagator

Abstract The rooted maps theory, a branch of the theory of homology, is shown to be a powerful tool for investigating the topological properties of Feynman diagrams, related to the single particle propagator in the quantum many-body systems. The numerical correspondence between the number of this class of Feynman diagrams as a function of perturbative order and the number of rooted maps as a function of the number of edges is studied. A graphical procedure to associate Feynman diagrams and rooted maps is then stated. Finally, starting from rooted maps principles, an original definition of the genus of a Feynman diagram, which totally differs from the usual one, is given.

scholarly journals Monte Carlo and renormalization-group effective potentials in scalar field theories

1995 ◽  
Vol 51 (12) ◽  
pp. 7017-7025 ◽  
Author(s):  
J. R. Shepard ◽  
V. Dmitrašinović ◽  
J. A. McNeil
Keyword(s):  
Monte Carlo ◽  
Renormalization Group ◽  
Scalar Field ◽  
Field Theories ◽  
Effective Potentials

scholarly journals Canonical Quantization of the Scalar Field: The Measure Theoretic Perspective

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
José Velhinho
Keyword(s):  
Scalar Field ◽  
Canonical Quantization ◽  
Field Theories ◽  
Quantum Fields ◽  
Theoretical Methods ◽  
Local Properties ◽  
Free Scalar ◽  
Free Fields ◽  
Field Behaviour

This review is devoted to measure theoretical methods in the canonical quantization of scalar field theories. We present in some detail the canonical quantization of the free scalar field. We study the measures associated with the free fields and present two characterizations of the support of these measures. The first characterization concerns local properties of the quantum fields, whereas for the second one we introduce a sequence of variables that test the field behaviour at large distances, thus allowing distinguishing between the typical quantum fields associated with different values of the mass.

scholarly journals Extended multi-scalar field theories in $$(1+1)$$ dimensions

2020 ◽  
Vol 80 (12) ◽  
Author(s):  
A. R. Aguirre ◽  
E. S. Souza
Keyword(s):  
Scalar Field ◽  
Linear Stability ◽  
Explicit Construction ◽  
Field Theories ◽  
Extension Method ◽  
Stability Properties ◽  
Field Systems

AbstractWe present the explicit construction of some multi-scalar field theories in $$(1+1$$ ( 1 + 1 ) dimensions supporting BPS (Bogomol’nyi–Prasad–Sommerfield) kink solutions. The construction is based on the ideas of the so-called extension method. In particular, several new interesting two-scalar and three-scalar field theories are explicitly constructed from non-trivial couplings between well-known one-scalar field theories. The BPS solutions of the original one-field systems will be also BPS solutions of the multi-scalar system by construction, and therefore we will analyse their linear stability properties for the constructed models.

scholarly journals Simulation of Scalar Field Theories with Complex Actions

2019 ◽  
Author(s):  
Michael Ogilvie ◽  
Leandro Medina
Keyword(s):  
Scalar Field ◽  
Field Theories
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