Renormalization scheme ambiguities in the models with more than one coupling

2020 ◽  
Vol 98 (1) ◽  
pp. 76-80
Author(s):  
D.G.C. McKeon ◽  
Chenguang Zhao
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Renormalization Group ◽  
Standard Model ◽  
Physical Process ◽  
Renormalization Scheme ◽  
Quantum Field ◽  
Loop Order ◽  
Massless Limit ◽  
The Standard Model

The process of renormalization to eliminate divergences arising in quantum field theory is not uniquely defined; one can always perform a finite renormalization, rendering finite perturbative results ambiguous. The consequences of making such finite renormalizations have been examined in the case of there being one or two couplings. In this paper, we consider how finite renormalizations can affect more general models in which there are more than two couplings. In particular, we consider the massless limit of the Standard Model in which there are essentially five couplings. We show that in this model (when neglecting all mass parameters) if we use mass independent renormalization, then the renormalization group β-functions are not unique beyond one-loop order, that it is not in general possible to eliminate all terms beyond certain order for all these β-functions, but that for a physical process, all contributions beyond one-loop order can be subsumed into the β-functions.

The Higgs impact on Einstein’s gravity: The Einstein–Kraichnan quantum gravity

2020 ◽  
Vol 35 (02n03) ◽  
pp. 2040012
Author(s):  
M. D. Maia ◽  
V. B. Bezerra
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Standard Model ◽  
Quantum Gravity ◽  
Higgs Mechanism ◽  
Quantum Field ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Fundamental Interactions ◽  
The Standard Model

An updated review of Kraichnan’s derivation of Einstein’s equations from quantum field theory is presented, including the period after the discovery of the Higgs mechanism and the inclusion of gravitation within the Standard Model of Fundamental Interactions.

scholarly journals Magnetic monopoles in field theory and cosmology

2012 ◽  
Vol 370 (1981) ◽  
pp. 5705-5717 ◽  
Author(s):  
Arttu Rajantie
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Standard Model ◽  
Particle Physics ◽  
Magnetic Monopoles ◽  
Beyond The Standard Model ◽  
Quantum Field ◽  
Magnetic Systems ◽  
The Standard Model

The existence of magnetic monopoles is predicted by many theories of particle physics beyond the standard model. However, in spite of extensive searches, there is no experimental or observational sign of them. I review the role of magnetic monopoles in quantum field theory and discuss their implications for particle physics and cosmology. I also highlight their differences and similarities with monopoles found in frustrated magnetic systems.

scholarly journals Unification of gravity and quantum field theory from extended noncommutative geometry

2017 ◽  
Vol 32 (05) ◽  
pp. 1750030 ◽  
Author(s):  
Hefu Yu ◽  
Bo-Qiang Ma
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Standard Model ◽  
Gravity Field ◽  
Noncommutative Geometry ◽  
Coordinate Frame ◽  
Quantum Field ◽  
Gravity Effect ◽  
Frame Bundle ◽  
The Standard Model

We make biframe and quaternion extensions on the noncommutative geometry, and construct the biframe spacetime for the unification of gravity and quantum field theory (QFT). The extended geometry distinguishes between the ordinary spacetime based on the frame bundle and an extra non-coordinate spacetime based on the biframe bundle constructed by our extensions. The ordinary spacetime frame is globally flat and plays the role as the spacetime frame in which the fields of the Standard Model are defined. The non-coordinate frame is locally flat and is the gravity spacetime frame. The field defined in both frames of such “flat” biframe spacetime can be quantized and plays the role as the gravity field which couples with all the fields to connect the gravity effect with the Standard Model. Thus, we provide a geometric paradigm in which gravity and QFT can be unified.

scholarly journals STRING FIELD THEORY FROM QUANTUM GRAVITY

2013 ◽  
Vol 25 (10) ◽  
pp. 1343005
Author(s):  
LOUIS CRANE
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Standard Model ◽  
Quantum Gravity ◽  
String Field Theory ◽  
Neutrino Oscillations ◽  
Coupled Model ◽  
Dual Model ◽  
Quantum Field ◽  
The Standard Model

Recent work on neutrino oscillations suggests that the three generations of fermions in the standard model are related by representations of the finite group A(4), the group of symmetries of the tetrahedron. Motivated by this, we explore models which extend the EPRL model for quantum gravity by coupling it to a bosonic quantum field of representations of A(4). This coupling is possible because the representation category of A(4) is a module category over the representation categories used to construct the EPRL model. The vertex operators which interchange vacua in the resulting quantum field theory reproduce the bosons and fermions of the standard model, up to issues of symmetry breaking which we do not resolve. We are led to the hypothesis that physical particles in nature represent vacuum changing operators on a sea of invisible excitations which are only observable in the A(4) representation labels which govern the horizontal symmetry revealed in neutrino oscillations. The quantum field theory of the A(4) representations is just the dual model on the extended lattice of the Lie group E6, as explained by the quantum McKay correspondence of Frenkel, Jing and Wang. The coupled model can be thought of as string field theory, but propagating on a discretized quantum spacetime rather than a classical manifold.

scholarly journals Gauge Theories and the Standard Model

2020 ◽  
pp. 7-33
Author(s):  
Guido Altarelli ◽  
Stefano Forte
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Standard Model ◽  
Gauge Theories ◽  
Quantum Field ◽  
Link Type ◽  
The Standard Model ◽  
Strong Sector ◽  
Introductory Textbooks ◽  
Symmetry Structure

AbstractThis chapter, Chaps. 10.1007/978-3-030-38207-0_3 and 10.1007/978-3-030-38207-0_4 present a self-contained introduction to the Standard Model of fundamental interactions, which describes in the unified framework of gauge quantum field theories all of the fundamental forces of nature but gravity: the strong, weak, and electromagnetic interactions. This set of chapters thus provides both an introduction to the Standard Model, and to quantum field theory at an intermediate level. The union of the three chapters can be taken as a masters’ level course reference, and it requires as a prerequisite an elementary knowledge of quantum field theory, at the level of many introductory textbooks, such as Vol. 1 of Aitchison-Hey, or, at a somewhat more advanced level, Maggiore. The treatment is subdivided into three parts, each corresponding to an individual chapter, with more advanced field theory topics introduced along the way as needed. Specifically, this chapter presents the general structure of the Standard Model, its field content, and symmetry structure. This involves an introduction to non-abelian gauge theories both at the classical and quantum level. Also, it involves a discussion of spontaneous symmetry breaking and the Higgs mechanism, that play a crucial role in the architecture of the Standard Model, and their interplay with the quantization of gauge theories. Chapter 10.1007/978-3-030-38207-0_3 then presents the electroweak sector of the Standard Model. This requires introducing the concepts of CP violation and mixing, and of radiative corrections. Finally, Chap. 10.1007/978-3-030-38207-0_4 presents the strong sector of the theory, which requires a more detailed treatment of renormalization and the renormalization group.

scholarly journals ON FLAVOR CONSERVATION IN WEAK INTERACTION DECAYS INVOLVING MIXED NEUTRINOS

2010 ◽  
Vol 25 (22) ◽  
pp. 4179-4194 ◽  
Author(s):  
MASSIMO BLASONE ◽  
ANTONIO CAPOLUPO ◽  
CHUENG-RYONG JI ◽  
GIUSEPPE VITIELLO
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Standard Model ◽  
Weak Interaction ◽  
Tree Level ◽  
Quantum Field ◽  
Interaction Processes ◽  
Lepton Charge ◽  
The Standard Model ◽  
Short Time

In the context of quantum field theory (QFT), we compute the amplitudes of weak interaction processes such as W+ →e+ + νe and W+ →e+ + νμ by using different representations of flavor states for mixed neutrinos. Analyzing the short time limit of the above amplitudes, we find that the neutrino states defined in QFT as eigenstates of the flavor charges lead to results consistent with lepton charge conservation. On the contrary, the Pontecorvo flavor states produce a violation of lepton charge in the vertex, which is in contrast with what expected at tree level in the Standard Model.

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