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 QCD in a moving frame: an exploratory study

2018 ◽  
Vol 175 ◽  
pp. 14012 ◽  
Author(s):  
Mattia Dalla Brida ◽  
Leonardo Giusti ◽  
Michele Pepe
Keyword(s):  
Boundary Conditions ◽  
High Accuracy ◽  
Field Theories ◽  
Moving Frame ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Yang Mills ◽  
First Results ◽  
Set Up

The framework of shifted boundary conditions has proven to be a very powerful tool for the non-perturbative investigation of thermal quantum field theories. For instance, it has been successfully considered for the determination of the equation of state of SU(3) Yang-Mills theory with high accuracy. The set-up can be generalized to QCD and it is expected to lead to a similar breakthrough. We present first results for QCD with three flavours of non-perturbatively O(a)-improved Wilson fermions and shifted boundary conditions.

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 Edge states at phase boundaries and their stability

2016 ◽  
Vol 28 (09) ◽  
pp. 1650020 ◽  
Author(s):  
M. Asorey ◽  
A. P. Balachandran ◽  
J. M. Pérez-Pardo
Keyword(s):  
Boundary Conditions ◽  
Edge State ◽  
Field Theories ◽  
Kinetic Term ◽  
Quantum Field Theories ◽  
Dirac Fermions ◽  
Edge States ◽  
Abelian Gauge ◽  
The Stability ◽  
Physical Phenomena

We analyze the effects of Robin-like boundary conditions on different quantum field theories of spin 0, 1/2 and 1 on manifolds with boundaries. In particular, we show that these conditions often lead to the appearance of edge states. These states play a significant role in physical phenomena like quantum Hall effect and topological insulators. We prove in a rigorous way the existence of spectral lower bounds on the kinetic term of different Hamiltonians, even in the case of Abelian gauge fields where it is a non-elliptic differential operator. This guarantees the stability and consistency of massive field theories with masses larger than the lower bound of the kinetic term. Moreover, we find an upper bound for the deepest edge state. In the case of Abelian gauge theories, we analyze a generalization of Robin boundary conditions. For Dirac fermions, we analyze the cases of Atiyah–Patodi–Singer and chiral bag boundary conditions. The explicit dependence of the bounds on the boundary conditions and the size of the system is derived under general assumptions.

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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