排序方式: 共有15条查询结果,搜索用时 31 毫秒
1.
Daniel Maerten 《Annals of Global Analysis and Geometry》2007,32(4):391-414
We prove a Penrose-like inequality for the mass of a large class of constant mean curvature (CMC) asymptotically flat n-dimensional spin manifolds which satisfy the dominant energy condition and have a future converging, or past converging compact
and connected boundary of non-positive mean curvature and of positive Yamabe invariant. We prove that for every n ≥ 3 the mass is bounded from below by an expression involving the norm of the linear momentum, the volume of the boundary,
dimensionless geometric constants and some normalized Sobolev ratio. 相似文献
2.
Mauro Spera 《Journal of Functional Analysis》2003,197(1):110-139
In this paper, a rigorous construction of the S1-equivariant Dirac operator (i.e., Dirac-Ramond operator) on the space of (mean zero) loops in is given and its equivariant L2-index computed. Essential use is made of infinite tensor product representations of the canonical anticommutation relations algebra. 相似文献
3.
A cyclic evolution of a pure quantum state is characterized by a closed curve γ in the projective Hilbert space
, equipped with the Fubini-Study geometry. It is known that the geometric phase
for this evolution is given by the integral of the symplectic form of the Fubini-Study geometry over an arbitrary surface spanning γ. This result extends to an infinite-dimensional Hilbert space for a bosonic quantum field. We prove that
is bounded above by the infimum area over all surfaces spanning γ, and that the bound is attained if γ can be spanned by a holomorphic curve. Using an earlier result concerning the intrinsic Euclidean geometry of the coherent state submanifold
, we derive an expression for the geometric phase for a cyclic evolution amongst coherent states. We indicate how the intensity of a classical configuration can be inferred from the winding number of the exponential geometric phase about the origin in the complex plane. In the case of photon states we present group theoretic and 2-component spinor representations of
. We derive an expression for
in the case of a sequence of measurements such that the resulting states are coherent at each step, in terms of a sequence of projection operators. The situation in relation to some earlier experiments of Pancharatnam and Tomita–Chiao is explained. 相似文献
4.
5.
In this paper we redefine the well-known metric-affine Hilbert Lagrangian in terms of a spin connection and a spin-tetrad. On applying the Poincaré–Cartan method and using the geometry of gauge-natural bundles, a global gravitational superpotential is derived. On specializing to the case of the Kosmann lift, we recover the result originally found by Kijowski [Gen. Rel. Gravity 9 (1978) (10) 857] for the metric (natural) Hilbert Lagrangian. On choosing a different, suitable lift, we can also recover the Nester–Witten 2-form, which plays an important role in the energy positivity proof and in many quasi-local definitions of mass. 相似文献
6.
We construct examples of singular self-dual Zollfrei metrics explicitly, by patching a pair of Petean’s self-dual split-signature metrics. We prove that there is a natural one-to-one correspondence between these singular metrics and a certain set of embeddings of RP3 to CP3 which has one singular point. This embedding corresponds to an odd function on R that is rapidly decreasing and pure imaginary valued. The one-to-one correspondence is explicitly given by using the Radon transform. 相似文献
7.
In this paper we proceed into the next step of formalization of a consistent dual theory for mass dimension one spinors. This task is developed approaching the two different and complementary aspects of such duals, clarifying its algebraic structure and the so called τ-deformation. The former regards the mathematical equivalence of the recent proposed Lorentz preserving dual with the duals of algebraic spinors, from Clifford algebras, showing the consistency and generality of the new dual. Moreover, by revealing its automorphism structure, the hole of the τ-deformation and contrasting the action group orbits with other Lorentz breaking scenarios, we argue that the new mass dimension one dual theory is placed over solid and consistent basis. 相似文献
8.
Saskia Kind 《International Journal of Theoretical Physics》2008,47(12):3341-3390
Spinor relativity is a unified field theory, which derives gravitational and electromagnetic fields as well as a spinor field
from the geometry of an eight-dimensional complex and ‘chiral’ manifold. The structure of the theory is analogous to that
of general relativity: it is based on a metric with invariance group GL(ℂ2), which combines the Lorentz group with electromagnetic U(1), and the dynamics is determined by an action, which is an integral of a curvature scalar and does not contain coupling
constants. The theory is related to physics on spacetime by the assumption of a symmetry-breaking ground state such that a
four-dimensional submanifold with classical properties arises. In the vicinity of the ground state, the scale of which is
of Planck order, the equation system of spinor relativity reduces to the usual Einstein and Maxwell equations describing gravitational
and electromagnetic fields coupled to a Dirac spinor field, which satisfies a non-linear equation; an additional equation
relates the electromagnetic field to the polarization of the ground state condensate. 相似文献
9.
Nigel Hitchin 《Journal of Geometry and Physics》1997,23(3-4):287-300
The equation (Schlesinger's equation) for the isomonodromic deformations of an (SL (2, C) connection with four simple poles on the projective line is shown to describe a holomorphic projective structure on a surface. The space of geodesics of this structure is, by a primitive version of twistor theory, a two-dimensional complex Poisson manifold containing complete rational curves. The Poisson structure degenerates on a divisor and it is shown that the complement of the divisor is a symplectic manifold which can be identified with the quotient of the moduli space of representations of a free group on three generators in SL (2,
) by the action of a braid group. 相似文献
10.
Q. Duret 《Annals of Physics》2010,325(10):2041-2074
Starting from Wigner’s symmetry representation theorem, we give a general account of discrete symmetries (parity P, charge conjugation C, time-reversal T), focusing on fermions in Quantum Field Theory. We provide the rules of transformation of Weyl spinors, both at the classical level (grassmanian wave functions) and quantum level (operators). Making use of Wightman’s definition of invariance, we outline ambiguities linked to the notion of classical fermionic Lagrangian. We then present the general constraints cast by these transformations and their products on the propagator of the simplest among coupled fermionic system, the one made with one fermion and its antifermion. Last, we put in correspondence the propagation of C eigenstates (Majorana fermions) and the criteria cast on their propagator by C and CP invariance. 相似文献