Geometric Modular Action and Spontaneous Symmetry Breaking
نویسندگان
چکیده
We study spontaneous symmetry breaking for field algebras on Minkowski space in the presence of a condition of geometric modular action (CGMA) proposed earlier as a selection criterion for vacuum states on general space–times. We show that any internal symmetry group must commute with the representation of the Poincaré group (whose existence is assured by the CGMA) and each translation-invariant vector is also Poincaré invariant. The subspace of these vectors can be centrally decomposed into pure invariant states and the CGMA holds in the resulting sectors. As positivity of the energy is not assumed, similar results may be expected to hold for other space–times.
منابع مشابه
Noncommutative Geometric Gauge Theory from Superconnections
Noncommutative geometric gauge theory is reconstructed based on the superconnection concept. The bosonic action of the Connes-Lott model including the symmetry breaking Higgs sector is obtained by using a new generalized derivative, which consists of the usual 1-form exterior derivative plus an extra element called the matrix derivative, for the curvatures. We first derive the matrix derivative...
متن کاملSpontaneous Symmetry Breaking and Reflectionless Scattering Data
We consider the question which potentials in the action of a (1+1) dimensional scalar field theory allowing for spontaneous symmetry breaking have quantum fluctuations corresponding to reflectionless scattering data. The general problem of restoration from known scattering data is formulated and a number of explicit examples is given. Only certain sets of reflectionless scattering data correspo...
متن کاملSpontaneous Lorentz Symmetry Breaking by Anti-Symmetric Tensor Field
We study the spontaneous Lorentz symmetry breaking in a field theoretical model in (2+1)-dimension, inspired by string theory. This model is a gauge theory of an anti-symmetric tensor field and a vector field (photon). The Nambu-Goldstone (NG) boson for the spontaneous Lorentz symmetry breaking is identified with the unphysical massless photon in the covariant quantization. We also discuss an a...
متن کاملSpontaneous symmetry breaking in the Higgs mechanism
The Higgs mechanism is very powerful: it furnishes a description of the electroweak theory in the Standard Model which has a convincing experimental verification. But although the Higgs mechanism had been applied successfully, the conceptual background is not clear. The Higgs mechanism is often presented as spontaneous breaking of a local gauge symmetry. But a local gauge symmetry is rooted in ...
متن کاملSpatial Patterning with the Rule of Normal Neighbors
Based on developmental biology’s Rule of Normal Neighbors, we develop a new mechanism for spatial patterning, exhibiting spontaneous symmetry breaking, regeneration, and approximate scale invariance. The desired pattern is represented as a topological adjacency graph, yielding an energy function that cells minimize through local interactions. Combined with a controller manipulating cells’ mecha...
متن کامل