scholarly journals Elimination of Primitive Divergents from Field Theory by Means of Complex Coupling Constants

1973 ◽  
Vol 26 (6) ◽  
pp. 703
Author(s):  
AF Nicholson
Keyword(s):  
Field Theory ◽  
Matrix Element ◽  
Spinor Field ◽  
Scalar Fields ◽  
Coupling Constants ◽  
Quantum Fields ◽  
Iteration Theory ◽  
Spinor Fields ◽  
S Matrix ◽  
Physical Particle

LSZ. iteration theory is extended to accommodate quantum fields coupled by complex constants, while retaining a positive metric and a Hermitian Hamiltonian. Interpolating and particle (~in, out) fields are linked by an operator U(t) which is nonunitary, so that Haag's theorem may be avoided. It is shown that U(t) may be rendered sufficiently well-behaved as t -+ � 00 to allow development of the iteration series for the T function. For certain combinations of fields the coupling constants and masses can then be chosen so as to eliminate the primitive divergents from the iteration series for any S-matrix element. The theory is illustrated by two models: four spinor plus two scalar fields, and the electromagnetic plus several spinor fields. In the second model not every spinor field corresponds to a stable physical particle, and the LSZ formalism is extended to allow for this.

Stability of renormalization group fixed points and decay of correlations

2019 ◽  
pp. 101-110
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Fixed Points ◽  
Gradient Flow ◽  
Scalar Fields ◽  
Effective Field ◽  
Coupling Constants ◽  
Critical Systems ◽  
Universal Properties ◽  
General Physical

Chapter 7 is devoted to a discussion of the renormalization group (RG) flow when the effective field theory that describes universal properties of critical phenomena depends on several coupling constants. The universal properties of a large class of macroscopic phase transitions with short range interactions can be described by statistical field theories involving scalar fields with quartic interactions. The simplest critical systems have an O(N) orthogonal symmetry and, therefore, the corresponding field theory has only one quartic interaction. However, in more general physical systems, the flow of quartic interactions is more complicated. This chapter examines these systems from the RG viewpoint. RG beta functions are shown to generate a gradient flow. Some examples illustrate the notion of emergent symmetry. The local stability of fixed points is related to the value of the scaling field dimension.

Canonical quantization of free fields

2021 ◽  
pp. 70-98
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Field Theory ◽  
Quantum Theory ◽  
Electromagnetic Fields ◽  
Classical Theory ◽  
Canonical Quantization ◽  
Classical Mechanics ◽  
Scalar Fields ◽  
Complex Scalar ◽  
Spinor Fields ◽  
Free Fields

This chapter discusses canonical quantization in field theory and shows how the notion of a particle arises within the framework of the concept of a field. Canonical quantization is the process of constructing a quantum theory on the basis of a classical theory. The chapter briefly considers the main elements of this procedure, starting from its simplest version in classical mechanics. It first describes the general principles of canonical quantization and then provides concrete examples. The examples include the canonical quantization of free real scalar fields, free complex scalar fields, free spinor fields and free electromagnetic fields.

ON A PHASE STRUCTURE OF A TWO-DIMENSIONAL (φ2)2 FIELD THEORY

1989 ◽  
Vol 04 (18) ◽  
pp. 4977-4990 ◽  
Author(s):  
G. V. EFIMOV
Keyword(s):  
Field Theory ◽  
Phase Transitions ◽  
Phase Structure ◽  
Weak Coupling ◽  
Scalar Fields ◽  
Perturbation Series ◽  
Coupling Constants ◽  
Two Dimensional ◽  
Effective Coupling ◽  
Two Phases

Two models of scalar fields with the interaction Lagrangians gφ4 and [Formula: see text] are considered in ℝ2. There are phase transitions in these models for a certain g = gc. It is shown that the spontaneous symmetry breaking takes place for g > gc. The description of the two phases for g < gc and g > gc is given. The effective coupling constants in perturbation series are less than unity for both the phases so that these models describe the systems with weak coupling. In the second model the "Goldstone" particles have nonzero masses in the phase g > gc.

scholarly journals Quintessence and tachyon dark energy in interaction with dark matter: Observational constraints and model selection

2020 ◽  
Vol 29 (08) ◽  
pp. 2050057
Author(s):  
Sandro M. R. Micheletti
Keyword(s):  
Field Theory ◽  
Dark Energy ◽  
Scalar Fields ◽  
Coupling Constants ◽  
Observational Constraints ◽  
Acoustic Oscillations ◽  
Distance Information ◽  
New Agegraphic Dark Energy ◽  
Text Model ◽  
Baryonic Acoustic Oscillations

We derive two field theory models of interacting dark energy, one in which dark energy is associated with the quintessence and another in which it is associated with the tachyon. In both, instead of choosing arbitrarily the potential of scalar fields, these are specified implicitly by imposing that the dark energy fields must behave as the new agegraphic dark energy. The resulting models are compared with the Pantheon supernovae sample, CMB distance information from Planck 2015 data, baryonic acoustic oscillations (BAO) and Hubble parameter data. For comparison, the noninteracting case and the [Formula: see text] model also are considered. By use of the AIC and BIC criteria, we have obtained strong evidence in favor of the two interacting models, and the coupling constants are nonvanishing at more than [Formula: see text] confidence level.

THE AFFINE TODA S-MATRICES vs PERTURBATION THEORY

1993 ◽  
Vol 08 (01) ◽  
pp. 115-134 ◽  
Author(s):  
RYU SASAKI ◽  
FREDDY PERMANA ZEN
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Fourth Order ◽  
Calculation Method ◽  
Coupling Constants ◽  
Matrix Approach ◽  
Bootstrap Equation ◽  
S Matrix ◽  
Complete Form ◽  
Toda Field Theory

We present perturbative calculations for the Affine Toda Field Theory (ATFT) S-matrices to the second order in the coupling constants for [Formula: see text] and [Formula: see text] in general, to the fourth order for [Formula: see text] theory as well as to the sixth order for [Formula: see text] theory. Conventional Feynman–Dyson calculation method and the dispersion approach are used to calculate the complete form of the perturbation amplitudes in contrast to the pole residues in previous papers. The results agree with those S-matrices obtained in the S-matrix approach, namely those based on analyticity, unitarity, crossing and bootstrap equation.

scholarly journals Existence of multiple vortices in supersymmetric gauge field theory

2012 ◽  
Vol 468 (2148) ◽  
pp. 3923-3946 ◽  
Author(s):  
Shouxin Chen ◽  
Yisong Yang
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Extra Dimension ◽  
Existence And Uniqueness ◽  
Scalar Fields ◽  
Brane World ◽  
Coupling Constants ◽  
Gauge Field Theory ◽  
Vortex Solution ◽  
Supersymmetric Gauge

Two sharp existence and uniqueness theorems are presented for solutions of multiple vortices arising in a six-dimensional brane-world supersymmetric gauge field theory under the general gauge symmetry group G = U (1)× SU ( N ) and with N Higgs scalar fields in the fundamental representation of G . Specifically, when the space of extra dimension is compact so that vortices are hosted in a 2-torus of volume | Ω |, the existence of a unique multiple vortex solution representing n 1 ,…, n N , respectively, prescribed vortices arising in the N species of the Higgs fields is established under the explicitly stated necessary and sufficient condition where e and g are the U (1) electromagnetic and SU ( N ) chromatic coupling constants, v measures the energy scale of broken symmetry and is the total vortex number; when the space of extra dimension is the full plane, the existence and uniqueness of an arbitrarily prescribed n -vortex solution of finite energy is always ensured. These vortices are governed by a system of nonlinear elliptic equations, which may be reformulated to allow a variational structure. Proofs of existence are then developed using the methods of calculus of variations.

Threshold behaviour in quantum field theory

1952 ◽  
Vol 210 (1102) ◽  
pp. 388-404 ◽  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Matrix Element ◽  
Rest Mass ◽  
Momentum Conservation ◽  
Quantum Field ◽  
Branch Points ◽  
Threshold Values ◽  
Physical Assumption ◽  
S Matrix

The elements of the S matrix are functions of the energies and momenta of a set of incident particles. For sufficiently high relative energies of the incident particles new particles of non-zero rest mass can be created. At the thresholds for such creation processes the S matrix will have a complicated behaviour. This behaviour is investigated when the S matrix is calculated by means of renormalized quantum field theory. For a typical matrix element there are thresholds of two main types. The first is a creation threshold below which the element is zero on account of energy-momentum conservation; mathematically this is due to a Dirac S function factor. The second is an interference threshold above which a competing process has non-zero probability. Interference thresholds are closely connected with the appearance of displaced poles in the integration. It is shown that a matrix element will always contain a term having a branch point at an interference threshold; the path of analytic continuation round these branch points is obtained from the physical assumption that particles interact through their retarded fields. Between the threshold values it is shown that the S matrix elements are analytic functions of the energies and momenta of the incident particles.

Quantum Fields

2020 ◽  
pp. 227-238
Author(s):  
Daniel Canarutto
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Brst Symmetry ◽  
Gauge Field Theory ◽  
Quantum Fields ◽  
Spinor Fields ◽  
Lagrangian Field Theory

The basics of a Lagrangian field theory of quantum fields are laid down by exploiting the differential geometric notions introduced through F-smoothness. Infinitesimal vertical symmetries and currents in this setting lead, in particular, to the notion of BRST symmetry. The above results are applied to a fairly detailed study of a sample gauge field theory which includes spinor fields and ghosts.

Towards Infrared Finite S-matrix in Quantum Field Theory

2021 ◽  
Author(s):  
Hayato Hirai
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
S Matrix

scholarly journals Classical black hole scattering from a worldline quantum field theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Gustav Mogull ◽  
Jan Plefka ◽  
Jan Steinhoff
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Black Hole ◽  
Quantum Field ◽  
Expectation Values ◽  
Path Integral Representation ◽  
S Matrix ◽  
Feynman Rules ◽  
Definition Of ◽  
Three Body

Abstract A precise link is derived between scalar-graviton S-matrix elements and expectation values of operators in a worldline quantum field theory (WQFT), both used to describe classical scattering of black holes. The link is formally provided by a worldline path integral representation of the graviton-dressed scalar propagator, which may be inserted into a traditional definition of the S-matrix in terms of time-ordered correlators. To calculate expectation values in the WQFT a new set of Feynman rules is introduced which treats the gravitational field hμν(x) and position $$ {x}_i^{\mu}\left({\tau}_i\right) $$ x i μ τ i of each black hole on equal footing. Using these both the 3PM three-body gravitational radiation 〈hμv(k)〉 and 2PM two-body deflection $$ \Delta {p}_i^{\mu } $$ Δ p i μ from classical black hole scattering events are obtained. The latter can also be obtained from the eikonal phase of a 2 → 2 scalar S-matrix, which we show corresponds to the free energy of the WQFT.

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