A new proof of Wigner's theorem

In our paper we present a new, elementary proof for Wigner's famous unitary-antiunitary theorem.     

A proof of the Nielsen-Ninomiya theorem

The Nielsen-Ninomiya theorem asserts the impossibility of constructing lattice models of non-selfinteracting chiral fermions. A new proof is given here. This proof fills a technical gap in the two proofs presented by the authors of the theorem. It also serves as prelude to an investigation of the chiral properties of the general lattice model.     

Heisenberg proof of the Balian-Low theorem

We give an alternate proof of the fact that a function generating a basis of coherent states must have an infinitely long tail in either position space or momentum space. Our argument is a very natural one in which the Heisenberg Uncertainty Principle enters directly.Supported in part by the National Science Foundation under Grant No. DMS 8603795.     

Euclidean proof of the Goldstone theorem

The Goldstone theorem in the formulation ofKastler,Robinson, andSwieca is proven in the framework of Euclidean quantum field theory. One utilizes that Schwinger functions have the cluster property in all directions.Supported by the National Science Foundation.     

Elementary applications of quantum-electrokinematics theorem

Summary A preceding quantum-electrokinematics theorem obtained directly from the equations of Maxwell and of Schr?dinger-Pauli, connects, by means of an arbitrary irrotational vector fieldF the wave function of a many-particle system, the internal scalar and vector potentials and the electric permittivity, with the current density and scalar potential, or voltage, on the surface of the system itself. In particular it shows the role of the current due to the particle spin. By means of proper choices ofF, it can be used to find old and new relations and results which, in general, would be harder to get by other methods. In the present work the theorem is used to compute a new expression of the output current of cylindrical two-terminal devices which, in its turn, is applied to a few elementary cases relevant to a single particle. They concern bounded systems, in stationary state, and the drift and spin currents, in non-stationary states, of a free electron and of an electron in a uniform and constant magnetic field. We obtain that a bounded electron cannot induce current at the output terminals and that, in more general terms, the results given by the new approach in the case of ?small? sizes of the system, are very different from those obtained by means of the classical electrodynamics, whereas, as has to happen according to the classical limit principle, they tend to coincide for ?great? sizes of the system itself. So, a not well-defined value of the spin component along the motion axis of a free electron generates a time-dependent fluctuation of the current proportional to its steady value. In the presence of a homogenous magnetic field, rather, the electron spin and its not well-defined value can generate steady and time-dependent contributions of the current, respectively. We also find that the spin acts on the current partition between two contiguous surfaces. The proposed applications, even they are elementary, can have interest because many phenomena in many-particle systems can be reduced to deal with the motion of a single particle.     

A short proof of a Kupershmidt-Wilson theorem

This is a short elementary proof of a statement originally observed by Adler, then pursued by the author, by Kupershmidt and Wilson, and in a more general setting by Drinfeld and Sokolov.     

A new proof of M. Herman's theorem

A new proof of the M. Herman theorem on the smooth conjugacy of a circle map is presented here. It is based on the thermodynamic representation of dynamical systems and the study of the ergodic properties for the corresponding radom variables.Dedicated to Walter Thirring on his 60^th birthday     

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     

State-independent proof of Kochen-Specker theorem with 13 rays

Quantum contextuality, as proved by Kochen and Specker, and also by Bell, should manifest itself in any state in any system with more than two distinguishable states and recently has been experimentally verified. However, for the simplest system capable of exhibiting contextuality, a qutrit, the quantum contextuality is verified only state dependently in experiment because too many (at least 31) observables are involved in all the known state-independent tests. Here we report an experimentally testable inequality involving only 13 observables that is satisfied by all noncontextual realistic models while being violated by all qutrit states. Thus our inequality facilitates a state-independent test of the quantum contextuality for an indivisible quantum system. We also provide a record-breaking state-independent proof of the Kochen-Specker theorem with 13 directions determined by 26 points on the surface of a magic cube.     

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 simple proof of the generalization of Israel's theorem

A simple proof of the generalization of the theorem of Israel concerning the uniqueness of the Schwarzschild black hole is presented.Dedicated to Achille Papapetrou on the occasion of his retirement.     

A superspace path integral proof of the Gauss-Bonnet-Chern theorem

A rigorous theory of integration in the space of paths in super space is developed, by extending Berezin's method of integration to spaces of anticommuting variables with an uncountably high dimension. A Feynmam-Kac-Ito formula for the heat kernel of a wide class of superspace differential operators is established. This formula is then used to make rigorous the supersummetric proofs of the Gauss-Bonnet-Chern theorem [1, 2].     

Alternate proof of the optical theorem for impenetrable targets

The optical theorem is proven for impenetrable targets without using the method of stationary phase. The proof depends upon the divergence theorem, the Helmholtz representation of the scattered field, and the law of cosines.     

A Simple proof of the generalized electrostatic Israel theorem

A simple proof of a generalization of the theorem of Israel concerning the uniqueness of the Reissner-Nordström black holes is presented. The present method is also applied to show, in the bosonic sector ofN=4-supergravity, the uniqueness of a static black hole solution found by Gibbons.Work supported by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich, Project No. 4961.     

A new proof of the propagation theorem forN-body quantum systems

A new proof of I. Sigal's and A. Soffer's propagation theorem is given. This theorem describes a large class of operators which are Kato-smooth with respect to anN-body Schrödinger operator.On leave from Division of Mathematical Methods in Physics, Warsaw University, Hoza 74, PL-00682 Warsaw, Poland     

An elementary proof for the non-bijective version of Wigner's theorem

The non-bijective version of Wigner's theorem states that a map which is defined on the set of self-adjoint, rank-one projections (or pure states) of a complex Hilbert space and which preserves the transition probability between any two elements, is induced by a linear or antilinear isometry. We present a completely new, elementary and very short proof of this famous theorem which is very important in quantum mechanics. We do not assume bijectivity of the mapping or separability of the underlying space like in many other proofs.     

关于卡诺定理证明的教学探讨

介绍并讨论了卡诺定理的一种新的证明方法，在这种方法中没有直接使用扳证法，证明过程中的各主要中间结果物理涵义清楚，直观，容易理解。     

A heat kernel proof of the index theorem for deformation quantization

Letters in Mathematical Physics - We give a heat kernel proof of the algebraic index theorem for deformation quantization with separation of variables on a pseudo-Kähler manifold. We use...