The Wightman axioms and the mass gap for weakly coupled (ϕ4)3 quantum field theories

1976 ◽  
Vol 97 (1) ◽  
pp. 80-135 ◽  
Author(s):  
Joel S Feldman ◽  
Konrad Osterwalder
Keyword(s):  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Mass Gap ◽  
Weakly Coupled ◽  
Wightman Axioms

BINDING ENERGIES IN WEAKLY COUPLED (2+1)-DIMENSIONAL QUANTUM FIELD THEORIES

1991 ◽  
Vol 06 (29) ◽  
pp. 2705-2711
Author(s):  
G. GAT ◽  
B. ROSENSTEIN
Keyword(s):  
Perturbation Theory ◽  
Binding Energy ◽  
Bound State ◽  
Binding Energies ◽  
Field Theories ◽  
General Question ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Weakly Coupled ◽  
Gross Neveu Model

We calculate the binding energy of the two-particle threshold bound state in the (2+1)-dimensional Gross-Neveu model. This model was recently shown to be renormalizable within the 1/N expansion. The binding energy is found to be ΔE=4mc-8Nf where m is the mass of the elementary fermion and Nf is the number of flavors. The general question of consistency of the perturbation theory within the framework of the Bethe-Salpeter equation is discussed.

BOUND STATE ENERGIES IN THE 1/N EXPANSION

1993 ◽  
Vol 08 (09) ◽  
pp. 1613-1628
Author(s):  
T. JAROSZEWICZ ◽  
P.S. KURZEPA
Keyword(s):  
Bound States ◽  
Symmetric Tensor ◽  
Bound State ◽  
Binding Energies ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Leading Order ◽  
3 Dimensional ◽  
Weakly Coupled

We derive and solve — in an arbitrary number of dimensions — Omnès-type equations for bound-state energies in weakly coupled quantum field theories. We show that, for theories defined in the 1/N expansion, these equations are exact to leading order in 1/N. We derive and discuss the weak coupling and nonrelativistic limits of the Omnès equations. We then calculate the binding energies and effective bound-state couplings in (1+1), (1+2) and (1+3)-dimensional O(N)-invariant ϕ4 theory. We consider both the scalar and symmetric tensor bound states.

scholarly journals Boundary effects in bosonic and fermionic field theories

2015 ◽  
Vol 12 (06) ◽  
pp. 1560004 ◽  
Author(s):  
M. Asorey ◽  
D. García-Alvarez ◽  
J. M. Muñoz-Castañeda
Keyword(s):  
Boundary Conditions ◽  
Fundamental Principle ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Edge States ◽  
Fermionic Field ◽  
Mass Gap ◽  
Physical Boundary ◽  
General Perspective

The dynamics of quantum field theories on bounded domains requires the introduction of boundary conditions on the quantum fields. We address the problem from a very general perspective by using charge conservation as a fundamental principle for scalar and fermionic quantum field theories. Unitarity arises as a consequence of the choice of charge preserving boundary conditions. This provides a powerful framework for the analysis of global geometrical and topological properties of the space of physical boundary conditions. Boundary conditions which allow the existence of edge states can only arise in theories with a mass gap which is also a physical requirement for topological insulators.

scholarly journals Global aspects of spaces of vacua

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Adar Sharon
Keyword(s):  
Closed Loop ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Strongly Coupled ◽  
Weakly Coupled

Abstract We study “vacuum crossing”, which occurs when the vacua of a theory are exchanged as we vary some periodic parameter θ in a closed loop. We show that vacuum crossing is a useful non-perturbative tool to study strongly-coupled quantum field theories, since finding vacuum crossing in a weakly-coupled regime of the theory can lead to nontrivial consequences in the strongly-coupled regime. We start by discussing a mechanism where vacuum crossing occurs due to an anomaly, and then discuss some applications of vacuum crossing in general. In particular, we argue that vacuum crossing can be used to check IR dualities and to look for emergent IR symmetries.

scholarly journals SYMMETRY PRINCIPLE PRESERVING AND INFINITY FREE REGULARIZATION AND RENORMALIZATION OF QUANTUM FIELD THEORIES AND THE MASS GAP

2003 ◽  
Vol 18 (29) ◽  
pp. 5363-5419 ◽  
Author(s):  
YUE-LIANG WU
Keyword(s):  
Symmetry Breaking ◽  
Gauge Invariance ◽  
Energy Scale ◽  
New Method ◽  
Field Theories ◽  
Parameter Method ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Mass Gap ◽  
Scaling Symmetry

Through defining irreducible loop integrals (ILI's), a set of consistency conditions for the regularized (quadratically and logarithmically) divergent ILI's are obtained to maintain the generalized Ward identities of gauge invariance in non-Abelian gauge theories. The ILI's of arbitrary loop graphs can be evaluated from the corresponding Feynman loop integrals by adopting an ultraviolet (UV) divergence preserving parameter method. Overlapping UV divergences are explicitly shown to be factorizable in the ILI's and be harmless via suitable subtractions. A new regularization and renormalization method is presented in the initial space–time dimension of the theory. The procedure respects unitarity and causality. Of interest, the method leads to an infinity free renormalization and meanwhile maintains the symmetry principles of the original theory except the intrinsic mass scale caused conformal scaling symmetry breaking and the anomaly induced symmetry breaking. Tadpole graphs of Yang–Mills gauge fields are found to play an essential role for maintaining manifest gauge invariance via cancellations of quadratically divergent ILI's. Quantum field theories (QFT's) regularized through the new method are well defined and governed by a physically meaningful characteristic energy scale (CES) Mc and a physically interesting sliding energy scale (SES) μs which can run from μs ~ Mc to a dynamically generated mass gap μs = μc or to μs = 0 in the absence of mass gap and infrared (IR) problem. For Mc → ∞, the initial UV divergent properties of QFT's are recovered and well-defined. In fact, the CES Mc and SES at μs = μc play the role of UV and IR cutoff energy scales respectively. It is strongly indicated that the conformal scaling symmetry and its breaking mechanism play an important role for understanding the mass gap and quark confinement. The new method is developed to be applicable for both underlying renormalizable QFT's and effective QFT's. It also leads to a set of conjectures on mathematically interesting numbers and functional limits which may provide deep insights in mathematics.

scholarly journals Formfactors of Relativistic Composite Particle Interactions in Unified Nonlinear Spinorfield Models

1985 ◽  
Vol 40 (7) ◽  
pp. 752-773
Author(s):  
H. Stumpf
Keyword(s):  
Composite Particle ◽  
Particle Interaction ◽  
High Energy ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Statistical Interpretation ◽  
Quantum Field ◽  
Mapping Procedure ◽  
Effective Dynamics ◽  
Rough Approximation

Unified nonlinear spinorfield models are self-regularizing quantum field theories in which all observable (elementary and non-elementary) particles are assumed to be bound states of fermionic preon fields. Due to their large masses the preons themselves are confined and below the threshold of preon production the effective dynamics of the model is only concerned with bound state reactions. In preceding papers a functional energy representation, the statistical interpretation and the dynamical equations were derived and the effective dynamics for preon-antipreon boson states and three preon-fermion states (with corresponding anti-fermions) was studied in the low energy limit. The transformation of the functional energy representation of the spinorfield into composite particle functional operators produced a hierarchy of effective interactions at the composite particle level, the leading terms of which are identical with the functional energy representation of a phenomenological boson-fermion coupling theory. In this paper these calculations are extended into the high energy range. This leads to formfactors for the composite particle interaction terms which are calculated in a rough approximation and which in principle are observable. In addition, the mathematical and physical interpretation of nonlocal quantum field theories and the meaning of the mapping procedure, its relativistic invariance etc. are discussed.

scholarly journals Categorification of algebraic quantum field theories

2021 ◽  
Vol 111 (2) ◽  
Author(s):  
Marco Benini ◽  
Marco Perin ◽  
Alexander Schenkel ◽  
Lukas Woike
Keyword(s):  
Universal Algebra ◽  
Finite Groups ◽  
Physical Interpretation ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Algebraic Quantum

AbstractThis paper develops a concept of 2-categorical algebraic quantum field theories (2AQFTs) that assign locally presentable linear categories to spacetimes. It is proven that ordinary AQFTs embed as a coreflective full 2-subcategory into the 2-category of 2AQFTs. Examples of 2AQFTs that do not come from ordinary AQFTs via this embedding are constructed by a local gauging construction for finite groups, which admits a physical interpretation in terms of orbifold theories. A categorification of Fredenhagen’s universal algebra is developed and also computed for simple examples of 2AQFTs.

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