We extend the Hopf algebra description of a simple quantum system given previously, to a more elaborate Hopf algebra, which is rich enough to encompass that related to a description of perturbative quantum field theory (pQFT). This provides a mathematical route from an algebraic description of non-relativistic, non-field theoretic quantum statistical mechanics to one of relativistic quantum fie...

In a recent paper [7], Conway and Kochen claim to have established that theories of the GRW type, i.e., of spontaneous wave function collapse, cannot be made relativistic. On the other hand, relativistic GRW-type theories have already been presented, in my recent paper [16] and by Dowker and Henson [8]. Here, I elucidate why these are not excluded by the arguments of Conway and Kochen. PACS: 03...

In this article, the axioms presented in the first one are reformulated according to the special theory of relativity. Using these axioms, quantum mechanic's relativistic equations are obtained in the presence of electromagnetic fields for both the density function and the probability amplitude. It is shown that, within the present theory's scope, Dirac's second order equation should be conside...

The path integral quantum-statistical approach to study the magnetic properties of the weakly relativistic interacting electron gas in the inhomogeneous magnetic eld is suggested. In the random phase approximation the thermodynamic potential is calculated. In the case of absolute zero the magnetization and nonlinear magnetic susceptibility of the system are found. Both Landau diamagnetism and P...

We provide a brief overview of the basic tools and concepts of quantum field theoretical scattering theory. This article is commissioned by the Encyclopedia of Mathematical Physics, edited by J.-P. Françoise, G. Naber and T.S. Tsun, to be published by the Elsevier publishing house. 1 Physical Motivation and Mathematical Setting The primary connection of relativistic quantum field theory to expe...

A classical statistical field theory hidden variable model for the quantized Klein-Gordon model is constructed that preserves relativistic signal locality and is relativistically covariant, but is at the same time relativistically nonlocal, paralleling the Hegerfeldt nonlocality of quantum theory. It is argued that the relativistic nonlocality of this model is acceptable to classical physics, b...

How do our ideas about quantum mechanics affect our understanding of spacetime? This familiar question leads to quantum gravity. This talk addressed a complementary question: How do our ideas about spacetime affect our understanding of quantum mechanics? Familiar non-relativistic quantum theory illustrates how quantum mechanics incorporates assumptions about spacetime. The Schrödinger equation ...

A central problem in quantum condensed matter physics is the critical theory governing the zero-temperature quantum phase transition between strongly renormalized Fermi liquids as found in heavy fermion intermetallics and possibly in high-critical temperature superconductors. We found that the mathematics of string theory is capable of describing such fermionic quantum critical states. Using th...

This is the first of a two-part introduction to some interpretive questions that arise in connection with quantum field theories (QFTs). Some of these questions are continuous with those familiar from the discussion of ordinary non-relativistic quantum mechanics (QM). For example, questions about locality can be rigorously posed and fruitfully pursued within the framework of QFT. A stark disana...

In this work the electromagnetic radius and the polarizability of the mesons are obtained by use of the effective Lagrangians constructed on the one hand with taking into account of general principles of the relativistic quantum field theory and on the other hand with taking into account of the compound relativistic model meson representation. Also using a relativistic constituent quark model b...