215 research outputs found
Light-Cone Expansion of the Dirac Sea in the Presence of Chiral and Scalar Potentials
We study the Dirac sea in the presence of external chiral and
scalar/pseudoscalar potentials. In preparation, a method is developed for
calculating the advanced and retarded Green's functions in an expansion around
the light cone. For this, we first expand all Feynman diagrams and then
explicitly sum up the perturbation series. The light-cone expansion expresses
the Green's functions as an infinite sum of line integrals over the external
potential and its partial derivatives.
The Dirac sea is decomposed into a causal and a non-causal contribution. The
causal contribution has a light-cone expansion which is closely related to the
light-cone expansion of the Green's functions; it describes the singular
behavior of the Dirac sea in terms of nested line integrals along the light
cone. The non-causal contribution, on the other hand, is, to every order in
perturbation theory, a smooth function in position space.Comment: 59 pages, LaTeX (published version
The Principle of the Fermionic Projector: An Approach for Quantum Gravity?
In this short article we introduce the mathematical framework of the
principle of the fermionic projector and set up a variational principle in
discrete space-time. The underlying physical principles are discussed. We
outline the connection to the continuum theory and state recent results. In the
last two sections, we speculate on how it might be possible to describe quantum
gravity within this framework.Comment: 18 pages, LaTeX, few typos corrected (published version
Light-Cone Expansion of the Dirac Sea to First Order in the External Potential
The perturbation of the Dirac sea to first order in the external potential is
calculated in an expansion around the light cone. It is shown that the
perturbation consists of a causal contribution, which describes the singular
behavior of the Dirac sea on the light cone and contains bounded line integrals
over the potential and its partial derivatives, and a non-causal contribution,
which is a smooth function. As a preparatory step, we construct a formal
solution of the inhomogeneous Klein-Gordon equation in terms of an infinite
series of line integrals.
More generally, the method presented can be used for an explicit analysis of
Feynman diagrams of the Dirac, Klein-Gordon, and wave equations in position
space.Comment: 28 pages, typo in eq. (B.2) correcte
Fermion Systems in Discrete Space-Time
Fermion systems in discrete space-time are introduced as a model for physics
on the Planck scale. We set up a variational principle which describes a
non-local interaction of all fermions. This variational principle is symmetric
under permutations of the discrete space-time points. We explain how for
minimizers of the variational principle, the fermions spontaneously break this
permutation symmetry and induce on space-time a discrete causal structure.Comment: 8 pages, LaTeX, few typos corrected (published version
Fermion Systems in Discrete Space-Time - Outer Symmetries and Spontaneous Symmetry Breaking
A systematic procedure is developed for constructing fermion systems in
discrete space-time which have a given outer symmetry. The construction is
illustrated by simple examples. For the symmetric group, we derive constraints
for the number of particles. In the physically interesting case of many
particles and even more space-time points, this result shows that the
permutation symmetry of discrete space-time is always spontaneously broken by
the fermionic projector.Comment: 43 pages, LaTeX, few typos corrected (published version
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