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V. M. Risti? M. M. Radulovi? T. B. Miladinovi? 《International Journal of Theoretical Physics》2011,50(11):3602-3609
In this paper we suggest that theories treating two interacting objects in a different manner (for instance electromagnetic
field of a laser classically, and the interacting atom as a quantum object) should be called “mixed”. Mixed theories are not
so rare in Physics. One just should look at the whole area of Atomic, Molecular and Optical Physics in which mixed theories
are often used, and, also, theories including quantum object interacting with classical surroundings that are the subject
of our present discussion: the field of Quantum decoherence, when applied to resolving the dilemma should classical trajectories
be used in explaining the Stern-Gerlach experiment or not. Consequently we are proving one improved corollary to Noether’s
theorem, stating that mixed theories are not supporting the law of conservation of angular momentum and spin, as they are
not based on the isotropy of space-time. 相似文献
3.
The original proof of Gleason’s Theorem is very complicated and therefore, any result that can be derived also without the
use of Gleason’s Theorem is welcome both in mathematics and mathematical physics. In this paper we reprove some known results
that had originally been proved by the use of Gleason’s Theorem, e.g. that on the quantum logic ℒ(H) of all closed subspaces of a Hilbert space H, dim H≥3, there is no finitely additive state whose range is countably infinite. In particular, if dim H=n, then on ℒ(H) there is a unique discrete state, namely m(A)=dim A/dim H, A∈ℒ(H).
Dedicated to Pekka J. Lahti on the occasion of his 60th birthday.
The paper has been supported by the Center of Excellence SAS–Physics of Information–I/2/2005, the grant VEGA No. 2/6088/26
SAV, by Science and Technology Assistance Agency under the contract APVV-0071-06, Bratislava, Slovakia. 相似文献
4.
The constructions appearing in the formality theorem by Kontsevich [9] and Tamarkin [13] are first made locally. In these references, sufficient conditions are given to globalize the formality maps. Kontsevich formality maps satisfy these conditions. In this Letter, we show that Tamarkins maps can also be constructed so as to satify these conditions, thus can be globalized. 相似文献
5.
Extensions of Lieb’s Concavity Theorem 总被引:3,自引:1,他引:2
Frank Hansen 《Journal of statistical physics》2006,124(1):87-101
The operator function (A,B)→ Trf(A,B)(K
*)K, defined in pairs of bounded self-adjoint operators in the domain of a function f of two real variables, is convex for every Hilbert Schmidt operator K, if and only if f is operator convex. We obtain, as a special case, a new proof of Lieb’s concavity theorem for the function (A,B)→ TrA
p
K
*
B
q
K, where p and q are non-negative numbers with sum p+q ≤ 1. In addition, we prove concavity of the operator function
in its natural domain D
2(μ1,μ2), cf. Definition 3. 相似文献
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7.
Mihály Weiner 《Communications in Mathematical Physics》2011,305(2):469-485
Under natural conditions (such as split property and geometric modular action of wedge algebras) it is shown that the unitary
equivalence class of the net of local (von Neumann) algebras in the vacuum sector associated to double cones with bases on
a fixed space-like hyperplane completely determines an algebraic QFT model. More precisely, if for two models there is a unitary
connecting all of these algebras, then — without assuming that this unitary also connects their respective vacuum states or spacetime symmetry representations — it follows
that the two models are equivalent. This result might be viewed as an algebraic version of the celebrated theorem of Rudolf
Haag about problems regarding the so-called “interaction-picture” in QFT. Original motivation of the author for finding such
an algebraic version came from conformal chiral QFT. Both the chiral case as well as a related conjecture about standard half-sided
modular inclusions will be also discussed. 相似文献
8.
We consider the survival probability of a state that evolves according to the Schrödinger dynamics generated by a self-adjoint operator H. We deduce from a classical result of Salem that upper bounds for the Hausdorff dimension of a set supporting the spectral measure associated with the initial state imply lower bounds on a subsequence of time scales for the survival probability. This general phenomenon is illustrated with applications to the Fibonacci operator and the critical almost Mathieu operator. In particular, this gives the first quantitative dynamical bound for the critical almost Mathieu operator. 相似文献
9.
Louis Vervoort 《Foundations of Physics》2013,43(6):769-791
Bell’s theorem admits several interpretations or ‘solutions’, the standard interpretation being ‘indeterminism’, a next one ‘nonlocality’. In this article two further solutions are investigated, termed here ‘superdeterminism’ and ‘supercorrelation’. The former is especially interesting for philosophical reasons, if only because it is always rejected on the basis of extra-physical arguments. The latter, supercorrelation, will be studied here by investigating model systems that can mimic it, namely spin lattices. It is shown that in these systems the Bell inequality can be violated, even if they are local according to usual definitions. Violation of the Bell inequality is retraced to violation of ‘measurement independence’. These results emphasize the importance of studying the premises of the Bell inequality in realistic systems. 相似文献
10.
José L. Cereceda 《Foundations of Physics Letters》1999,12(3):211-231
In this paper the failure of Hardy's nonlocality proof for the class of maximally entangled states is considered. A detailed analysis shows that the incompatibility of the Hardy equations for this class of states physically originates from the fact that the existence of quantum perfect correlations for the three pairs of two-valued observables (D
11, D
21), (D
11, D
22), and (D
12, D
21) [in the sense of having with certainty equal (different) readings for a joint measurement of any one of the pairs (D
11, D
21), (D
11, D
22), and (D
12, D
21)], necessarily entails perfect correlation for the pair of observables (D
12, D
22) [in the sense of having with certainty equal (different) readings for a joint measurement of the pair (D
12, D
22)]. Indeed, the set of these four perfect correlations is found to satisfy the CHSH inequality, and then no violations of local realism will arise for the maximally entangled state as far as the four observables D
ij, i,j = 1 or 2, are concerned. The connection between this fact and the impossibility for the quantum mechanical predictions to give the maximum possible theoretical violation of the CHSH inequality is pointed out. Moreover, it is generally proved that the fulfillment of all the Hardy nonlocality conditions necessarily entails a violation of the resulting CHSH inequality. The largest violation of this latter inequality is determined. 相似文献
11.
In this paper we introduce a new notion of λ ?order homogeneous operators on the nuclear algebra of white noise operators. Then, we give their Fock expansion in terms of quantum white noise (QWN) fields \(\{a_{t},\: a^{*}_{t}\, ; \; t\in \mathbb {R}\}\). The quantum extension of the scaling transform enables us to prove Euler’s theorem in quantum white noise setting. 相似文献
12.
Ed Seidewitz 《Foundations of Physics》2017,47(3):355-374
Under the normal assumptions of quantum field theory, Haag’s theorem states that any field unitarily equivalent to a free field must itself be a free field. Unfortunately, the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field but must still account for interactions. Thus, the traditional perturbative derivation of the scattering matrix in quantum field theory is mathematically ill defined. Nevertheless, perturbative quantum field theory is currently the only practical approach for addressing scattering for realistic interactions, and it has been spectacularly successful in making empirical predictions. This paper explains this success by showing that Haag’s Theorem can be avoided when quantum field theory is formulated using an invariant, fifth path parameter in addition to the usual four position parameters, such that the Dyson perturbation expansion for the scattering matrix can still be reproduced. As a result, the parameterized formalism provides a consistent foundation for the interpretation of quantum field theory as used in practice and, perhaps, for better dealing with other mathematical issues. 相似文献
13.
Given a globally hyperbolic spacetime M, we show the existence of a smooth spacelike Cauchy hypersurface S and, thus, a global diffeomorphism between M and ×S.The second-named author has been partially supported by a MCyT-FEDER Grant BFM2001-2871-C04-01. 相似文献
14.
A proof of Bell’s theorem without inequalities is presented in which distant local setups do not need to be aligned, since
the required perfect correlations are achieved for any local rotation of the local setups. 相似文献
15.
We prove the analogue of Weyl’s law for a noncommutative Riemannian manifold, namely the noncommutative two torus ${\mathbb{T}_{\theta}^{2}}$ equipped with a general translation invariant conformal structure and a Weyl conformal factor. This is achieved by studying the asymptotic distribution of the eigenvalues of the perturbed Laplacian on ${\mathbb{T}_{\theta}^{2}}$ . We also prove the analogue of Connes’ trace theorem by showing that the Dixmier trace and a noncommutative residue coincide on pseudodifferential operators of order ?2 on ${\mathbb{T}_{\theta}^{2}}$ . 相似文献
16.
Joe Henson 《Foundations of Physics》2013,43(8):1008-1038
This paper addresses arguments that “separability” is an assumption of Bell’s theorem, and that abandoning this assumption in our interpretation of quantum mechanics (a position sometimes referred to as “holism”) will allow us to restore a satisfying locality principle. Separability here means that all events associated to the union of some set of disjoint regions are combinations of events associated to each region taken separately. In this article, it is shown that: (a) localised events can be consistently defined without implying separability; (b) the definition of Bell’s locality condition does not rely on separability in any way; (c) the proof of Bell’s theorem does not use separability as an assumption. If, inspired by considerations of non-separability, the assumptions of Bell’s theorem are weakened, what remains no longer embodies the locality principle. Teller’s argument for “relational holism” and Howard’s arguments concerning separability are criticised in the light of these results. Howard’s claim that Einstein grounded his arguments on the incompleteness of QM with a separability assumption is also challenged. Instead, Einstein is better interpreted as referring merely to the existence of localised events. Finally, it is argued that Bell rejected the idea that separability is an assumption of his theorem. 相似文献
17.
K. A. Kirkpatrick 《Foundations of Physics Letters》2006,19(1):95-102
A concise presentation of Schrödinger's ancilla theorem (Proc. Camb. Phil. Soc. 32, 446 (1936)) and its several recent rediscoveries. 相似文献
18.
Julian Barbour 《Foundations of Physics》2010,40(9-10):1263-1284
Two definitions of Mach’s principle are proposed. Both are related to gauge theory, are universal in scope and amount to formulations of causality that take into account the relational nature of position, time, and size. One of them leads directly to general relativity and may have relevance to the problem of creating a quantum theory of gravity. 相似文献
19.
Alexey E. Rastegin 《International Journal of Theoretical Physics》2012,51(4):1300-1315
We discuss those relations for entropies of two quantum measurements that do not follow from the Riesz theorem and its varieties.
As measures of an uncertainty, both the Rényi entropies and Tsallis entropies are utilized. It is assumed that values of entropic
parameters do not share the usual relation which is required for application of Riesz’s theorem. As is shown, the question
is quite reduced to estimating from below the sum or the product of norm-like functions of two generated probability distributions.
The considered approach is developed in details within the two examples. In the first example, entropic uncertainty relations
are given for a pair of spin-1/2 components along two non-orthogonal axes. The second example deals with two measurements
for state discrimination. The former projective measurement is assigned to the Helstrom scheme, the second POVM is related
to the B92 protocol of quantum key distribution. 相似文献