Recently, unexpected relations between unrelated physical quantities such as Hall viscosity, conductivity and angular momentum have been proposed for certain condensed matter systems with broken parity. We derive the quantum field theory Ward identities originated from area preserving as well as conformal transformations for relativistic as well as non-relativistic systems. The relations among these physical quantities depend on the symmetries of the system. A special cases yields the well known relation: Hall viscosity is half the angular momentum.

We introduce a new 2+1 dimensional topological current that is identically conserved and whose charge is equal to the Euler character of the two dimensional spacelike foliations. The existence of this current allows us to introduce new Chern-Simons-type terms in the effective field theories describing relativistic quantum Hall states and (2+1) dimensional superfluids. In the quantum Hall case, this current provides the natural relativistic generalization of the Wen-Zee term, required to characterize the shift and Hall viscosity in quantum Hall systems. For the superfluid case this term is required to have nonzero Hall viscosity and to describe superfluids with non s-wave pairing.

 

It is often said that soliton contributions to perturbative processes in QFT are exponentially suppressed by a form-factor. We will provide a derivation of this form-factor by studying the soliton-antisoliton pair-production amplitude. This reduces to the calculation of a matrix element in the quantum mechanics on the soliton moduli space. We will investigate the conditions under which the latter leads to exponential suppression. We will also discuss how it suggests that the instanton-solitons of N = 2 SYM in 5D will not be suppressed and the implications for its relation to the (2,0) theory in 6D.

The introduction of a thin conducting shell into vacuum changes the electromagnetic mode structure.  This modifies the zero point energy of space, so that there is an energy associated with the shape and size of the object.   The value of this Casimir self-energy has hitherto been known only for the sphere and the infinite cylinder. However,  Balian and Duplantier have given a route to its calculation for an arbitrary shape.   I will explain their method and my implementation of it, and give some examples: ellipsoid, doughnut, pancake, cucumber, and cube with rounded edges.

Abstract: The properties of the ground-state spin 3/2 baryon decuplet have been studied for many years with limited success. For instance, while the masses, decay aspects, and other physical observables of some of these particles have been ascertained reasonably well, the magnetic moments of most are yet to be determined. In fact, only the magnetic moment of the strangeness S= -3 decuplet member has been accurately determined and that is because it is composed of valence quarks that make its lifetime substantially longer—via weak interaction decay—than any of its decuplet partners which possess strong interaction decay channels. We utilize equal‑time commutation relations involving at most one current density which are valid in broken flavor symmetry and valid even when the Lagrangian is not known or cannot be constructed. We also utilize the infinite‑momentum frame and broken flavor symmetry characterized by the existence of physical on‑mass‑shell hadron annihilation operators and their creation operator counterparts which produce physical states when acting on the vacuum and where physical on‑mass‑shell hadron annihilation operators are related linearly under flavor transformations to representation annihilation operators. This of course has the consequence that physical states—which do not belong to irreducible representations—are linear combinations of representation states which do belong to irreducible representations plus nonlinear corrective terms in the infinite-momentum frame. We note that the particular Lorentz frame that one uses when analyzing current‑algebraic sum rules does not matter when flavor symmetry is exact and is strictly a matter of taste and calculational convenience. When one uses non‑perturbative current-algebraic sum rules in broken flavor symmetry and the infinite‑momentum frame as we do, the choice of frame is paramount since nonlinear corrective terms are best calculated in a frame where mass differences are de‑emphasized.