Quantum field theory: An effective theory

2019 ◽  
pp. 111-136
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Particle Physics ◽  
Statistical Physics ◽  
Mass Scale ◽  
Effective Field ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Microscopic Scale ◽  
Linear Sigma Models

Chapter 8 discusses effective field theory. This concept is inspired by the theory of critical phenomena in statistical physics and based on renormalization group ideas. The basic idea behind effective field theory is that one starts from a microscopic model involving an infinite number of fluctuating degrees of freedom whose interactions are characterized by a microscopic scale and in which, as a result of interactions, a length that is much larger than the microscopic scale, or, equivalently, a mass much smaller than the characteristic mass scale of the initial model, is generated. The chapter illustrates this topic with examples. It also stresses that all quantum field theories as applied to particle physics or statistical physics are only effective (i.e. not fundamental) theories. Besides the problem of a phi4 type field theory with a large mass field, two more complicated examples are discussed: the Gross–Neveu and the non–linear sigma models.

scholarly journals THE CONDITION 0 < Z < 1 AND AN INTRINSIC MASS SCALE IN QUANTUM FIELD THEORY

2001 ◽  
Vol 16 (27) ◽  
pp. 4489-4497 ◽  
Author(s):  
SATISH D. JOGLEKAR
Keyword(s):  
Field Theory ◽  
Mass Scale ◽  
Effective Field ◽  
Energy Scale ◽  
Field Theories ◽  
Beyond The Standard Model ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Nonlocal Formulation ◽  
Intrinsic Scale

In this work, we suggest a viewpoint that leads to an intrinsic mass scale in quantum field theories. This viewpoint is fairly independent of dynamical details of a QFT and does not rely on any particular framework to go beyond the Standard Model. We use the setting of the nonlocal quantum field theories (NLQFT) with a finite scale parameter Λ, which are unitary for finite Λ. We propose that the condition 0 < Z < 1 (wherever proven) can be rigorously implemented/imposed in such theories and that it implies the existence of a mass scale Λ that can be determined from this condition. We derive the nonlocal analog of the above relation (which is a finite relation in NLQFT) and demonstrate that it can be arrived at only from general principles. We further propose that the nonlocal formulation should be looked as an effective field theory that incorporates the effect of dynamics beyond an energy scale and which breaks at the intrinsic scale Λ so obtained. Beyond this scale it should be replaced by another (perhaps, a more fundamental) theory. We provide a heuristic justification for this viewpoint.

Effective Field Theory in Particle Physics and Cosmology

2020 ◽  
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Particle Physics ◽  
Large Scale ◽  
Effective Field ◽  
Effective Theory ◽  
Soft Collinear Effective Theory ◽  
Multiple Length Scales ◽  
Cosmological Observations ◽  
Standard Models

Effective field theory (EFT) is a general method for describing quantum systems with multiple-length scales in a tractable fashion. It allows us to perform precise calculations in established models (such as the standard models of particle physics and cosmology), as well as to concisely parametrize possible effects from physics beyond the standard models. EFTs have become key tools in the theoretical analysis of particle physics experiments and cosmological observations, despite being absent from many textbooks. This volume aims to provide a comprehensive introduction to many of the EFTs in use today, and covers topics that include large-scale structure, WIMPs, dark matter, heavy quark effective theory, flavour physics, soft-collinear effective theory, and more.

scholarly journals Diluted mass gap in strongly coupled non-local Yang-Mills

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Marco Frasca ◽  
Anish Ghoshal
Keyword(s):  
Field Theory ◽  
Particle Physics ◽  
Mass Scale ◽  
Local Theory ◽  
Quantum Field ◽  
Strongly Coupled ◽  
Yang Mills ◽  
Mass Gap ◽  
Non Local ◽  
Non Locality

Abstract We investigate the non-perturbative regimes in the class of non-Abelian theories that have been proposed as an ultraviolet completion of 4-D Quantum Field Theory (QFT) generalizing the kinetic energy operators to an infinite series of higher-order derivatives inspired by string field theory. We prove that, at the non-perturbative level, the physical spectrum of the theory is actually corrected by the “infinite number of derivatives” present in the action. We derive a set of Dyson-Schwinger equations in differential form, for correlation functions till two-points, the solution for which are known in the local theory. We obtain that just like in the local theory, the non-local counterpart displays a mass gap, depending also on the mass scale of non-locality, and show that it is damped in the deep UV asymptotically. We point out some possible implications of our result in particle physics and cosmology and discuss aspects of non-local QCD-like scenarios.

scholarly journals Effective theories with dark matter applications

2021 ◽  
Author(s):  
Subhaditya Bhattacharya ◽  
José Wudka
Keyword(s):  
Field Theory ◽  
Dark Matter ◽  
Effective Field Theory ◽  
Particle Physics ◽  
High Energy ◽  
New Physics ◽  
Effective Field ◽  
The Subject ◽  
Effective Theories ◽  
Detailed Nature

Standard Model (SM) of particle physics has achieved enormous success in describing the interactions among the known fundamental constituents of nature, yet it fails to describe phenomena for which there is very strong experimental evidence, such as the existence of dark matter, and which point to the existence of new physics not included in that model; beyond its existence, experimental data, however, have not provided clear indications as to the nature of that new physics. The effective field theory (EFT) approach, the subject of this review, is designed for this type of situations; it provides a consistent and unbiased framework within which to study new physics effects whose existence is expected but whose detailed nature is known very imperfectly. We will provide a description of this approach together with a discussion of some of its basic theoretical aspects. We then consider applications to high-energy phenomenology and conclude with a discussion of the application of EFT techniques to the study of dark matter physics and its possible interactions with the SM. In several of the applications we also briefly discuss specific models that are ultraviolet complete and may realize the effects described by the EFT.

scholarly journals SMEFT analysis of vector boson scattering and diboson data from the LHC Run II

2021 ◽  
Vol 81 (6) ◽  
Author(s):  
Jacob J. Ethier ◽  
Raquel Gomez-Ambrosio ◽  
Giacomo Magni ◽  
Juan Rojo
Keyword(s):  
Field Theory ◽  
Cross Sections ◽  
Effective Field Theory ◽  
Particle Physics ◽  
Vector Boson ◽  
Effective Field ◽  
High Luminosity ◽  
Complementary Information ◽  
Electroweak Sector ◽  
Vector Boson Scattering

AbstractWe present a systematic interpretation of vector boson scattering (VBS) and diboson measurements from the LHC in the framework of the dimension-six standard model effective field theory (SMEFT). We consider all available measurements of VBS fiducial cross-sections and differential distributions from ATLAS and CMS, in most cases based on the full Run II luminosity, and use them to constrain 16 independent directions in the dimension-six EFT parameter space. Compared to the diboson measurements, we find that VBS provides complementary information on several of the operators relevant for the description of the electroweak sector. We also quantify the ultimate EFT reach of VBS measurements via dedicated projections for the high luminosity LHC. Our results motivate the integration of VBS processes in future global SMEFT interpretations of particle physics data.

scholarly journals AN APPLICATION OF NEUTRIX CALCULUS TO QUANTUM FIELD THEORY

2006 ◽  
Vol 21 (02) ◽  
pp. 297-312 ◽  
Author(s):  
Y. JACK NG ◽  
H. VAN DAM
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Effective Field Theories ◽  
Quantum Gravity ◽  
Asymptotic Series ◽  
Effective Field ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Neutrix Calculus

Neutrices are additive groups of negligible functions that do not contain any constants except 0. Their calculus was developed by van der Corput and Hadamard in connection with asymptotic series and divergent integrals. We apply neutrix calculus to quantum field theory, obtaining finite renormalizations in the loop calculations. For renormalizable quantum field theories, we recover all the usual physically observable results. One possible advantage of the neutrix framework is that effective field theories can be accommodated. Quantum gravity theories will then appear to be more manageable.

scholarly journals Effective theories and infinite idealizations: a challenge for scientific realism

Synthese ◽  
2020 ◽  
Author(s):  
Sébastien Rivat
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Structural Features ◽  
Effective Field ◽  
Good News ◽  
Quantum Field ◽  
Specific Context ◽  
Ontological Commitments ◽  
Effective Theories ◽  
Made In

Abstract Williams and J. Fraser have recently argued that effective field theory methods enable scientific realists to make more reliable ontological commitments in quantum field theory (QFT) than those commonly made. In this paper, I show that the interpretative relevance of these methods extends beyond the specific context of QFT by identifying common structural features shared by effective theories across physics. In particular, I argue that effective theories are best characterized by the fact that they contain intrinsic empirical limitations, and I extract from their structure one central interpretative constraint for making more reliable ontological commitments in different subfields of physics. While this is in principle good news, this constraint still raises a challenge for scientific realists in some contexts, and I bring the point home by focusing on Williams’s and J. Fraser’s defense of selective realism in QFT.

scholarly journals On the development of effective field theory

2021 ◽  
Author(s):  
Steven Weinberg
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Particle Physics ◽  
Effective Field ◽  
Early History ◽  
First Century ◽  
Field Theories ◽  
Theory Approach ◽  
Seminar Series ◽  
History Of

AbstractEditor’s note: One of the most important developments in theoretical particle physics at the end of the 20th century and beginning of the twenty-first century has been the development of effective field theories (EFTs). Pursuing an effective field theory approach is a methodology for constructing theories, where a set of core principles is agreed upon, such as Lorentz symmetry and unitarity, and all possible interactions consistent with them are then compulsory in the theory. The utility of this approach to particle physics (and beyond) is wide ranging and undisputed, as evidenced by the recent formation of the international seminar series All Things EFT (Talks in the series can be viewed at https://www.youtube.com/channel/UC1_KF6kdJFoDEcLgpcegwCQ (accessed 21 December 2020).) which brings together each week the worldwide community of EFT practitioners. The text below is a lightly edited version of the talk given by Prof. Weinberg on September 30, 2020, which inaugurated the series. The talk reviews some of the early history of EFTs from the perspective of its pioneer and concludes with a discussion of EFT implications for future discovery.

scholarly journals Optical theorem and indefinite metric in λϕ4 delta-theory

2020 ◽  
Vol 35 (33) ◽  
pp. 2050214
Author(s):  
Ricardo Avila ◽  
Carlos M. Reyes
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Coupling Parameter ◽  
Effective Field ◽  
Optical Theorem ◽  
Indefinite Metric ◽  
Quantum Field ◽  
Scalar Model ◽  
Loop Order ◽  
Interaction Term

A class of effective field theory called delta-theory, which improves ultraviolet divergences in quantum field theory, is considered. We focus on a scalar model with a quartic self-interaction term and construct the delta theory by applying the so-called delta prescription. We quantize the theory using field variables that diagonalize the Lagrangian, which include a standard scalar field and a ghost or negative norm state. As well known, the indefinite metric may lead to the loss of unitary of the [Formula: see text]-matrix. We study the optical theorem and check the validity of the cutting equations for three processes at one-loop order, and found suppressed violations of unitarity in the delta coupling parameter of the order of [Formula: see text].

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