A specific class of gauge theories is geometrically described in terms of fermions. In particular, it is shown how the geometrical frame presented naturally includes spontaneous symmetry breaking of Yang-Mills gauge theories without making use of a Higgs potential. In more physical terms, it is shown that the Yukawa coupling of fermions, together with gravity, necessarily yields a symmetry reduction provided the fermionic mass is considered as a globally well-defined concept. The structure of this symmetry breaking is shown to be compatible with the symmetry breaking that is induced by the Higgs potential of the minimal Standard Model. As a consequence, it is shown that the fermionic mass has a simple geometrical interpretation in terms of curvature and that the (semi-classical)"fermionic vacuum" determines the intrinsic geometry of space-time. We also discuss the issue of "fermion doubling" in some detail and introduce a specific projection onto the "physical sub-space" that is motivated from the Standard Model.
The Dirac-Bergmann algorithm is a recipe for converting a theory with a singular Lagrangian into a constrained Hamiltonian system. Constrained Hamiltonian systems include gauge theories -- general relativity, electromagnetism, Yang Mills, string theory, etc. The Dirac-Bergmann algorithm is elegant but at the same time rather complicated. It consists of a large number of logical steps linked together by a subtle chain of reasoning. Examples of the Dirac-Bergmann algorithm found in the literature are designed to isolate and illustrate just one or two of those logical steps. In this paper I analy…
D-branes in Generalized Geometry and Dirac-Born-Infeld Action
本文的目的是在广义几何的框架下建立Dirac Born Infeld（DBI）作用量并阐明其对称性。D-膜定义为静态规范中标量场和规范场被同等对待的狄拉克结构。我们推导出相应的广义李导数的非线性同态和B场规范变换，并表明DBI行动下的非线性实现的对称性下的所有类型的非线性同态和B场规范变换是不变的。因此，我们不仅可以把D-膜上的标量场，而且可以把D-膜上的规范场解释为广义南武-戈德斯通玻色子。
An upper bound of the relative entanglement entropy of thermal states at an inverse temperature $β$ of linear, massive Klein-Gordon and Dirac quantum field theories across two regions, separated by a nonzero distance $d$ in a Cauchy hypersurface of an ultrastatic (spin-)spacetime has been computed. This entanglement measure is bounded by a negative constant times $\ln | \tanh (πd/ 2 β) |$ which signifies power law decay for asymptotic $d$ where the exponent depends on $β< \infty$.
One of the main tools used to understand both qualitative and quantitative spectral behaviour of periodic and almost periodic Schrödinger operators is the method of gauge transform. In this paper, we extend this method to an abstract setting, thus allowing for greater flexibility in its applications that include, among others, matrix-valued operators. In particular, we obtain asymptotic expansions for the density of states of certain almost periodic systems of elliptic operators, including systems of Dirac type. We also prove that a range of periodic systems including the two-dimensional Dirac…
