The problem of chiral symmetry breaking in QED in a strong magnetic field is briefly reviewed. Recent progress on issues regarding the gauge fixing independence of the dynamically generated fermion mass is discussed. Gauge theories play an important role in our understanding of a wide variety of phenomena in many areas of physics, ranging from the descriptions of fundamental interactions in ele...

We consider in detail an approach (proposed by the author earlier) where quantum states are described by elements of a linear space over a Galois field, and operators of physical quantities by linear operators in this space. The notion of Galois fields (which is extremely simple and elegant) is discussed in detail and we also discuss the conditions when our description gives the same prediction...

We identify exact excitation content of the intermediate states for the oneparticle Green’s functions, spin-spin and (charge) density-density correlation functions of the periodic one-dimensional t-J model with inverse square exchange. The excitations consist of neutral S = 1/2 spinons and spinless (charge −e) holons with semionic fractional statistics, and bosonic (charge +2e) “anti-holons” wh...

That symmetry is fundamental to modern physics is a view frequently expressed by physicists. In his popular expositions Steven Weinberg, for example, has aimed above all to communicate his conviction that ‘symmetries are fundamental, and possibly all that one needs to learn about the physical world beyond quantum mechanics itself’.1 His fellow particle physicist Abdus Salam has argued similarly...

We reconsider the problem of absence of continuous symmetry breaking for systems of point particles in R. Assuming smoothness and suitable decay of the interaction, we show that each tempered Gibbs measure is invariant under translations. If the particles exhibit internal degrees of freedom with continuous symmetries, the latter are also preserved. The proof is elementary and avoids the use of ...

It is known that optical activities can perform rotations. It is shown that the rotation, if modulated by attenuations, can perform symmetry operations of Wigner’s little group which dictates the internal space-time symmetries of elementary particles.

The algebraic method of renormalization is applied to the standard model of electroweak interactions. We present the most important modifications compared to theories with simple groups. ∗ Presented at the DESY Zeuthen Workshop on Elementary Particle Theory “Loops and Legs in Gauge Theories”, Rheinsberg, Germany, April 19-24, 1998. (1) ALGEBRAIC RENORMALIZATION OF THE ELECTROWEAK STANDARD MODEL