Feynman rules for Gauss's law

I work on a set of Feynman rules that were derived in order to incorporate the constraint of Gauss's law in the perturbation expansion of gauge field theories and calculate the interaction energy of two static sources. The constraint is implemented via a Lagrange multiplier field, $\lambda$, which, in the case of the non-Abelian theory, develops a radiatively generated effective potential term. After analysing the contributions of various solutions for $\lambda$, the confining properties and the various phases of the theory are discussed.Comment: 18 pages, 10 figure

Gravitational effects on critical Q-balls

In a cosmological phase transition in theories that admit Q-balls there is a value of the soliton charge above which the soliton becomes unstable and expands, converting space to the true vacuum, much like a critical bubble in the case of ordinary tunneling. Here I consider the effects of gravity on these solitons and I calculate the lowest gravitational corrections to the critical radius and charge.Comment: LaTeX, 8 pages, final version to appear in EP

Quantum-classical interactions through the path integral

I consider the case of two interacting scalar fields, \phi and \psi, and use the path integral formalism in order to treat the first classically and the second quantum-mechanically. I derive the Feynman rules and the resulting equation of motion for the classical field, which should be an improvement of the usual semi-classical procedure. As an application I use this method in order to enforce Gauss's law as a classical equation in a non-abelian gauge theory. I argue that the theory is renormalizable and equivalent to the usual Yang-Mills as far as the gauge field terms are concerned. There are additional terms in the effective action that depend on the Lagrange multiplier field \lambda that is used to enforce the constraint. These terms and their relation to the confining properties of the theory are discussed.Comment: 16 pages, LaTeX, 1 fig, final version to appear in PR

The quantum Yang-Mills theory

In axiomatic quantum field theory, the postulate of the uniqueness of the vacuum (a pure vacuum state) is independent of the other axioms and equivalent to the cluster decomposition property. The latter, however, implies a Coulomb or Yukawa attenuation of the interactions at growing distance, hence cannot accomodate the confining properties of the strong interaction. The solution of the Yang-Mills quantum theory given previously, uses an auxiliary field to incorporate Gauss's law, and demonstrates the existence of two separate vacua, the perturbative and the confining vacuum, therefore a mixed vacuum state, deriving confinement, as well as the related, expected properties of the strong interaction. The existence of multiple vacua is, in fact, expected by the axiomatic, algebraic quantum field theory, via the decomposition of the vacuum state to eigenspaces of the auxiliary field. The general vacuum state is a mixed quantum state and the cluster decomposition property does not hold. Because of the energy density difference between the two vacua, the physics of the strong interactions does not admit a Lagrangian description. I clarify the above remarks related to the previous solution of the Yang-Mills interaction, and conclude with some discussion, a criticism of a related mathematical problem, and some tentative comments regarding the spin-2 case.Comment: 15 page

A proposal for the Yang-Mills vacuum and mass gap

I examine a set of Feynman rules, and the resulting effective action, that were proposed in order to incorporate the constraint of Gauss's law in the perturbation expansion of gauge field theories. A set of solutions for the Lagrangian and Hamiltonian equations of motion in Minkowski space-time, as well as their stability, are investigated. A discussion of the Euclidean action, confinement, and the strong-CP problem is also included. The properties and symmetries of the perturbative and the confining vacuum are explored, as well as the possible transitions between them, and the relations with phenomenological models of the strong interactions.Comment: 21 pages, 5 figures, revised versio

The path integral measure, constraints and ghosts for massive gravitons with a cosmological constant

For massive gravity in a de Sitter background one encounters problems of stability when the curvature is larger than the graviton mass. I analyze this situation from the path integral point of view and show that it is related to the conformal factor problem of Euclidean quantum (massless) gravity. When a constraint for massive gravity is incorporated and the proper treatment of the path integral measure is taken into account one finds that, for particular choices of the DeWitt metric on the space of metrics (in fact, the same choices as in the massless case), one obtains the opposite bound on the graviton mass.Comment: LaTeX, 10 pages, to appear in Phys. Rev.