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991.
We present an axiomatic approach to Dirac's equation in General Relativity based on intrinsically covariant geometric structures. Structure groups and the related principal bundle formulation can be recovered by studying the automorphisms of the theory. Various aspects can be most neatly understood within this context, and a number of questions can be most properly addressed (specifically in view of the formulation of QFT on a curved background). In particular, we clarify the fact that the usual spinor structure can be weakened while retaining all essential physical aspects of the theory. 相似文献
992.
Wei Li 《Physics letters. A》2010,374(29):2957-1991
The strong Coulomb interaction between massless Dirac fermions can drive a semimetal-insulator transition in single-layer graphene by dynamically generating an excitonic fermion gap. There is a critical interaction strength λc that separates the semimetal phase from the insulator phase. We calculate the specific heat and susceptibility of the system and show that they exhibit distinct behaviors in the semimetal and insulator phases. 相似文献
993.
994.
Yoshihiro Fukumoto 《Journal of Mathematical Analysis and Applications》2005,309(2):674-685
The main purpose of this paper is to give a geometric interpretation of the reciprocity law of the Fourier-Dedekind sum given by M. Beck and S. Robins. In fact, the V-index of the spinc Dirac operator on the weighted projective space is equal to the dimension of the space of all weighted homogeneous polynomials of given degree, and this equality gives precisely the Beck-Robins reciprocity law. In this equality, the Fourier-Dedekind sums appear as the localization terms of the V-index of the spinc Dirac operators and have a relationship to the eta invariants of lens spaces. 相似文献
995.
E. O. Pozdeeva 《Theoretical and Mathematical Physics》2009,159(2):618-626
Using the Darboux transformation method, we construct a two-parameter family of exactly solvable Dirac Hamiltonians. We obtain
intertwining relations between various members of this family. We study the spectral properties of these Hamiltonians and
give explicit expressions for their eigenfunctions.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 159, No. 2, pp. 243–251, May, 2009. 相似文献
996.
P. Cerejeiras U. Khler F. Sommen 《Mathematical Methods in the Applied Sciences》2005,28(14):1715-1724
We consider parabolic Dirac operators which do not involve fractional derivatives and use them to show the solvability of the in‐stationary Navier–Stokes equations over time‐varying domains. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
997.
In this paper we consider periodic Dirac operators with skew-adjoint potentials in a large class of weighted Sobolev spaces. We characterize the smoothness of such potentials by asymptotic properties of the periodic spectrum of the corresponding Dirac operators. 相似文献
998.
The Seiberg-Witten monopole equations, and a new invariant for 4-manifolds which results from these equations, are introduced
in this paper. 相似文献
999.
We prove that Neumann, Dirichlet and regularity problems for divergence form elliptic equations in the half-space are well posed in L2 for small complex L∞ perturbations of a coefficient matrix which is either real symmetric, of block form or constant. All matrices are assumed to be independent of the transversal coordinate. We solve the Neumann, Dirichlet and regularity problems through a new boundary operator method which makes use of operators in the functional calculus of an underlaying first order Dirac type operator. We establish quadratic estimates for this Dirac operator, which implies that the associated Hardy projection operators are bounded and depend continuously on the coefficient matrix. We also prove that certain transmission problems for k-forms are well posed for small perturbations of block matrices. 相似文献
1000.
We carry out the spectral analysis of singular matrix valued perturbations of 3-dimensional Dirac operators with variable magnetic field of constant direction. Under suitable assumptions on the magnetic field and on the perturbations, we obtain a limiting absorption principle, we prove the absence of singular continuous spectrum in certain intervals and state properties of the point spectrum. Constant, periodic as well as diverging magnetic fields are covered, and Coulomb potentials up to the physical nuclear charge Z<137 are allowed. The importance of an internal-type operator (a 2-dimensional Dirac operator) is also revealed in our study. The proofs rely on commutator methods. 相似文献