New method for calculating binding energies in quantum mechanics and quantum field theories

1993 ◽  
Vol 70 (1) ◽  
pp. 5-8 ◽  
Author(s):  
G. Gat ◽  
B. Rosenstein
Keyword(s):  
Quantum Mechanics ◽  
Binding Energies ◽  
New Method ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field

scholarly journals ON A NEW METHOD FOR COMPUTING TRACE ANOMALIES

1994 ◽  
Vol 03 (01) ◽  
pp. 145-148 ◽  
Author(s):  
FIORENZO BASTIANELLI
Keyword(s):  
Heat Kernel ◽  
Path Integrals ◽  
New Method ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Particle Theory ◽  
Curved Spaces ◽  
Main Ideas

I describe a new method for computing trace anomalies in quantum field theories which makes use of path-integrals for particles moving in curved spaces. After presenting the main ideas of the method, I discuss how it is connected to the first quantized approach of particle theory and to heat kernel techniques.

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 On spontaneous wave function collapse and quantum field theory

2006 ◽  
Vol 462 (2070) ◽  
pp. 1897-1908 ◽  
Author(s):  
Roderich Tumulka
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Mathematical Structure ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Stochastic Evolution ◽  
Explicit Model ◽  
Natural Way ◽  
Grw Model

One way of obtaining a version of quantum mechanics without observers, and thus of solving the paradoxes of quantum mechanics, is to modify the Schrödinger evolution by implementing spontaneous collapses of the wave function. An explicit model of this kind was proposed in 1986 by Ghirardi, Rimini & Weber (GRW), involving a nonlinear, stochastic evolution of the wave function. We point out how, by focusing on the essential mathematical structure of the GRW model and a clear ontology, it can be generalized to (regularized) quantum field theories in a simple and natural way.

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.

CLASSICAL CELLULAR AUTOMATA AND QUANTUM FIELD THEORY

2010 ◽  
Vol 25 (23) ◽  
pp. 4385-4396 ◽  
Author(s):  
GERARD 'T HOOFT
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Cellular Automata ◽  
Essential Role ◽  
Gravitational Force ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Mathematical Relation

It is pointed out that a mathematical relation exists between cellular automata and quantum field theories. Although the proofs are far from perfect, they do suggest a new look at the origin of quantum mechanics, and an essential role for the gravitational force in these considerations is suspected.

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