A theorem concerning Goldstone fermions

For any given model Lagrangian with spontaneous super-symmetry breaking we give the composition of the expected Goldstone fermion in terms of fields in the model.     

A Berger-type theorem for metric connections with skew-symmetric torsion

We prove a Berger-type theorem which asserts that if the orthogonal subgroup generated by the torsion tensor (pulled back to a point by parallel transport) of a metric connection with skew-symmetric torsion is not transitive on the sphere, then the space must be locally isometric to a Lie group with a bi-invariant metric or its symmetric dual (we assume the space to be locally irreducible). We also prove that a (simple) Lie group with a bi-invariant metric admits only two flat metric connections with skew-symmetric torsion: the two flat canonical connections. In particular, we get a refinement of a well-known theorem of Cartan and Schouten. Finally, we show that the holonomy group of a metric connection with skew-symmetric torsion on these spaces generically coincides with the Riemannian holonomy.     

A new proof of the positive energy theorem

A new proof is given of the positive energy theorem of classical general relativity. Also, a new proof is given that there are no asymptotically Euclidean gravitational instantons. (These theorems have been proved previously, by a different method, by Schoen and Yau.) The relevance of these results to the stability of Minkowski space is discussed.Research partially supported by NSF Grant PHY78-01221     

A generalization of the Gel’fond theorem concerning number systems

The distribution law for the remainders in the expansion of reals in a special number system is obtained.     

The power counting theorem for Minkowski metric

Dyson's power counting theorem is proved for the case of Minkowski metric.The research reported in this paper was supported in part by the National Science Foundation.     

A no-go theorem concerning the enhancement of nuclear decays by intense radiation fields

It is shown that radiation fields well below the critical field strength cannot induce any noticeable enhancements of nuclear decay rates.     

Remarks on the reconstruction theorem for field theories with indefinite metric

The Wightman functions of a field theory with indefinite metric allow the reconstruction of a linear space with an indefinite sesquilinear form. It is investigated when this form is given by a bounded operator on a Hilbert space.     

On Witten's proof of the positive energy theorem

This paper gives a mathematically rigorous proof of the positive energy theorem using spinors. This completes and simplifies the original argument presented by Edward Witten. We clarify the geometric aspects of this argument and prove the necessary analytic theorems concerning the relevant Dirac operator.Supported in part by the National Science Foundation under Grant PHY79-16812Junior Fellow, Harvard University Society of Fellows     

Proof of the positive mass theorem. II

The positive mass theorem states that for a nontrivial isolated physical system, the total energy, which includes contributions from both matter and gravitation is positive. This assertion was demonstrated in our previous paper in the important case when the space-time admits a maximal slice. Here this assumption is removed and the general theorem is demonstrated. Abstracts of the results of this paper appeared in [11] and [13].     

A generalized positive energy theorem for spaces with asymptotic SUSY compactification

In this short note, we prove a generalized positive energy theorem for spaces with asymptotic SUSY compactification involving non-symmetric data. This work is motivated by the work of Dai [A positive mass theorem for spaces with asymptotic SUSY compactification, Comm. Math. Phys. 244 (2004) 335–345; A note on positive energy theorem for spaces with asymptotic SUSY compactification, 2004. arXiv:math-ph/0406006], Hertog–Horowitz–Maeda [Negative energy density in Calabi–Yau compactifications, JHEP 0305 (2003) 060], and Zhang [Angular momentum and positive mass theorem, Comm. Math. Phys. 206 (1999) 137–155].     

A theorem concerning twisted and untwisted partition functions in and lattice gauge theories

In order to get a clue to understanding the volume-dependence of vortex free energy (which is defined as the ratio of the twisted against the untwisted partition function), we investigate the relation between vortex free energies defined on lattices of different sizes. An equality is derived through a simple calculation which equates a general linear combination of vortex free energies defined on a lattice to that on a smaller lattice. The couplings in the denominator and in the numerator however shows a discrepancy, and we argue that it vanishes in the thermodynamic limit. Comparison between our result and the work of Tomboulis is also presented. In the appendix we carefully examine the proof of quark confinement by Tomboulis and summarize its loopholes.     

Symmetry transformations in indefinite metric spaces: A generalization of Wigner's theorem

We formulate and prove a generalization to indefinite metric spaces of Uhlhorn's version of Wigner's theorem.     

On a theorem of Titchmarsh-Neumark-Walter concerning absolutely continuous operators

We state and prove an extended version of a theorem of Titchmarsh-Neumark-Walter concerning absolutely continuous operators. Our proof is different, in fact, first we state a set of abstract criteria for absolute continuity. Then we illustrate how the JWKB-approximation method can be applied to verify this set of abstract criteria. This verification depends on detailed estimates that we shall prove in the second half of this paper.     

On the positive energy theorem involving mass and electromagnetic charges

A new theorem relating mass and charges is deduced, which can be applied to more general physical systems than those covered by the theorem of Gibbons and Hull [1].On leave from Instituto de Matématicas Astronomía y Física, Universidad Nacional de Córdoba, (5000) Córdoba, ArgentinaAlfred P. Sloan Fellow; supported in part by a grant from the National Science Foundation     

A Kerr-NUT metric

Using Galilean time and retarded distance as coordinates the usual Kerr metric is expressed in form similar to the Newman-Unti-Tamburino (NUT) metric. The combined Kerr-NUT metric is then investigated. In addition to the Kerr and NUT solutions of Einstein's equations, three other types of solutions are derived. These are (i) the radiating Kerr solution, (ii) the radiating NUT solution satisfyingR _ik= _{i k} , _i ⁱ = 0, and (iii) the associated Kerr solution satisfyingR _ik=0. Solution (i) is distinct from and simpler than the one reported earlier by two of us (P.C.V.; L.K.P) [6]. Solutions (ii) and (iii) give line elements which have the axis of symmetry as a singular line.     

Kochen-Specker theorem for a single qubit using positive operator-valued measures

A proof of the Kochen-Specker theorem for a single two-level system is presented. It employs five eight-element positive operator-valued measures and a simple algebraic reasoning based on the geometry of the dodecahedron.     

A nonstationary generalization of the Kerr-Newman metric

A new metric depending on three arbitrary parameters is presented by the method of complex coordinate transformations. It gives the gravitational field of a radiating rotating charged body. The metric is algebraically special of Petrov type II according to classification of the Weyl tensor, with a twisting, shear-free, null congruence identical to that of the Kerr-Newman metric. The new metric bears the same relation to the Kerr-Newman metric as the Bonner-Vaidya metric does to the Reissner-Nordstrom metric.