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ABSTRACT: An eight parameter family of the most general nonnegative quadruple probabilities is constructed for EPR-Bohm-Aharonov experiments when only 3 pairs of analyser settings are used. It is a simultaneous representation of 3 Bohr-incompatible experimental configurations valid for arbitrary quantum states. Comment: Typo corrected in abstract
07/2006;
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ABSTRACT: We study the problem of constructing a probability density in 2N-dimensional phase space which reproduces a given collection of $n$ joint probability distributions as marginals. Only distributions authorized by quantum mechanics, i.e. depending on a (complete) commuting set of $N$ variables, are considered. A diagrammatic or graph theoretic formulation of the problem is developed. We then exactly determine the set of ``admissible'' data, i.e. those types of data for which the problem always admits solutions. This is done in the case where the joint distributions originate from quantum mechanics as well as in the case where this constraint is not imposed. In particular, it is shown that a necessary (but not sufficient) condition for the existence of solutions is $n\leq N+1$. When the data are admissible and the quantum constraint is not imposed, the general solution for the phase space density is determined explicitly. For admissible data of a quantum origin, the general solution is given in certain (but not all) cases. In the remaining cases, only a subset of solutions is obtained.
03/2004;
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ABSTRACT: We address the classical and quantum marginal problems, namely the question of simultaneous realizability through a common probability density in phase space of a given set of compatible probability distributions. We consider only distributions authorized by quantum mechanics, i.e. those corresponding to complete commuting sets of observables. For four-dimensional phase space with position variables qi and momentum variables pj, we establish the two following points: i) given four compatible probabilities for (q1,q2), (q1,p2), (p1,q2) and (p1,p2), there does not always exist a positive phase space density rho({qi},{pj}) reproducing them as marginals; this settles a long standing conjecture; it is achieved by first deriving Bell-like inequalities in phase space which have their own theoretical and experimental interest. ii) given instead at most three compatible probabilities, there always exist an associated phase space density rho({qi},{pj}); the solution is not unique and its general form is worked out. These two points constitute our ``three marginal theorem''. Comment: 21 pages, Latex, no figures
05/2002;
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ABSTRACT: We derive ``Bell inequalities'' in four dimensional phase space and prove the
following ``three marginal theorem'' for phase space densities
$\rho(\overrightarrow{q},\overrightarrow{p})$, thus settling a long standing
conjecture : ``there exist quantum states for which more than three of the
quantum probability distributions for $(q_1,q_2)$, $(p_1,p_2)$, $(q_1,p_2)$ and
$(p_1,q_2)$ cannot be reproduced as marginals of a positive
$\rho(\overrightarrow{q},\overrightarrow{p})$''. We also construct the most
general positive $\rho(\overrightarrow{q},\overrightarrow{p})$ which reproduces
any three of the above quantum probability densities for arbitrary quantum
states. This is crucial for the construction of a maximally realistic quantum
theory.
05/2002;
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ABSTRACT: Quantum mechanically for the Bohm-Aharonov system of two spin-1/2 particles in a singlet state the polarisation correlation parameter is P(a, b) mod QM=( sigma 1.a sigma 2.b)=-a.b. For a class of hidden variable theories, including those with P(a, a)=-1, the authors formulate the Einstein-Bell locality condition and obtains a generalisation of Bell's inequality.
Journal of Physics A General Physics 01/2001; 12(7):1003.
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ABSTRACT: Gives a systematic method to construct exact non-spreading wave packed solution (lumps) of the Schrodinger equation for a charged particle in an electromagnetic field and of the nonlinear Schrodinger equation. The method yields new kinds of accelerating lumps with both rotational and translational motion, in contrast to the more familiar soliton solutions which have constant velocity. In particular, the authors find new normalisable coherent states for the harmonic oscillator and new normalisable lumps for a charged particle in a constant magnetic field plus an electric field with axial symmetry. The method can be applied to relativistic wave equations and classical field theories to find their lump solutions.
Journal of Physics A General Physics 12/1998; 14(11):2927.
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ABSTRACT: We recently constructed a causal quantum mechanics in 2 dim. phase space which is more realistic than the de Broglie-Bohm mechanics as it reproduces not just the position but also the momentum probability density of ordinary quantum theory. Here we present an even more ambitious construction in 2n dim. phase space. We conjecture that the causal Hamiltonian quantum mechanics presented here is `maximally realistic'. The positive definite phase space density reproduces as marginals the correct quantum probability densities of $n+1$ different complete commuting sets of observables (e.g. $\vec q$, $\vec p$ and $n-1$ other sets). In general the particle velocities do not coincide with the de Broglie-Bohm velocities. Comment: Published version
11/1998;
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ABSTRACT: : De Broglie and Bohm formulated a causal quantum mechanics with a phase space density whose integral over momentum reproduces the position probability density of usual statistical quantum theory. We propose a causal quantum theory with a joint probability distribution such that the separate probability distributions for position and momentum agree with usual quantum theory. Unlike the Wigner distribution the suggested distribution is positive definite and obeys the Liouville condition. ? e-mail: Shasanka@Cernvm.cern.ch On leave (and address after 4 November 1994) from Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400 005, India. CERN-TH.7481/94 1. Introduction. Present quantum theory does not make definite prediction of the value of an observable in an individual observation except in an eigenstate of the observable. Application of quantum rules to two separated systems which interacted in the past together with a local reality principle (Einstein locality) led E...
06/1998;
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ABSTRACT: Present quantum theory, which is statistical in nature, does not predict joint probability distribution of position and momentum because they are noncommuting. We propose a deterministic quantum theory which predicts a joint probability distribution such that the separate probability distributions for position and momentum agree with usual quantum theory. Unlike the Wigner distribution the suggested distribution is positive definite. The theory predicts a correlation between position and momentum in individual events.
03/1994;
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ABSTRACT: We show that the classical Nambu-Goto string inD dimensions admits Poincaré invariance ind dimensions (d⩽D) if (i)d − 2 of the transverse co-ordinatesx
i are periodic and the rest quasi-periodic involving a real orthogonal matrix with (D − d) (D − d − 1)/2 free parameters, or if (ii)d − 2 ofx
i obey Neumann and the rest obey a boundary condition involvingN free parameters, whereN=(D − d)2/2 ifD − d is even, andN=[(D − d)2 − 1]/2 ifD − d is odd.
Pramana 04/1986; 26(1):L85-L91. · 0.57 Impact Factor
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ABSTRACT: We consider a fermion of chargee confined to a spherical bag with a Dirac monopole of strengthg at its centre. We find that the boundary conditions making the lowest angular momentum hamiltonian self-adjoint are characterized
by a unitary matrixU, and the corresponding vacuum charge has a fractional part 2|eg|α/π where detU = -exp (2iα). Boundary conditions for conservation of helicity,CP, CT andPT are displayed. We demonstrate the possibility of a fractionally charged dyon whose interaction with a fermion conserves helicity.
We also show thatthe simultaneous validity of helicity, CP, CT and PT requires integer vacuum charge.
Pramana 04/1985; 24(4):611-618. · 0.57 Impact Factor
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ABSTRACT: We show that for a fermion in a bounded background potential in a finite box, eigenvalues of the total charge are independent
of whether the potential is solitonic and depend only on the boundary condition: half-odd integral or integral for charge
conjugation (C) invariant boundary conditions and an arbitrary fraction forC non-invariant boundary conditions. Fractional fermion numbers for infinite space Jackiw-Rebbi and Goldstone-Wilczek Hamiltonians
are reproduced in finite space by using boundary conditions different from the periodic ones of Rajaraman and Bell.
Pramana 04/1984; 23(3):333-342. · 0.57 Impact Factor
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ABSTRACT: Self-adjointness of the time-independent Aharonov-Bohm Hamiltonian is shown to allow a continuous family of different dynamics
including those following from Pauli's criterion of rotational invariance, Aharonov-Bohm criterion of single valuedness and
a version of Pauli's criterion appropriate to cylindrical symmetry suggested by Henneberger. A time-dependent fluxF(t) linking the Aharonov-Bohm solenoid leads to the time-dependent AB Hamiltonian. Explicit solutions in cases with and without
inaccessible regions for the charged particle rule out applicability of both versions of the Pauli criterion. The solutions
contain one time-independent parameter α, integer values of which correspond to single-valued wave functions. Any real (integer
or noninteger) value of α is allowed. Charge and current densities depend on α andF(t) only through the combination α−eF(t)/2π and lead to the conclusion that physical effects of changing the flux during an experiment can be understood as local
effects of the electric field inevitably associated with changing magnetic flux.
Si mostra che la qualità di essere autoaggiunta dell'hamiltoniana indipendente dal tempo di Aharonov-Bohm permette una famiglia
continua di dinamiche differenti che comprendono quelle che seguono dal criterio di Pauli dell'invarianza rotazionale, dal
criterio di Aharonov-Bohm del singolo valore e da una versione del criterio di Pauli appropriata alla simmetria cilindrica
suggerita da Henneberger. Un flussoF(t) dipendente del tempo che lega il solenoide di Aharonov-Bohm porta all'hamiltoniana AB dipendente dal tempo. Soluzioni esplicite
nei casi con e senza regioni inaccessibili per la particella carica escludono l'applicabilità di entrambe le versioni del
criterio di Pauli. Le soluzioni contengono un parametro indipendente del tempo α, i valori interi del quale corrispondono
a funzioni d'onda a valore singolo. Si ammette qualunque valore reale di α (intero o non intero). La densità di carica e di
corrente dipendono da α eF(t) solo attraverso la combinazione α−eF(t)/2π e portano alla conclusione che effetti fisici di cambiare il flusso durante un'esperimento possono essere considerati
come effetti locali del campo elettrico inevitabilmente associato con il cambiamento del flusso magnetico.
Показывается, что самосопряженность зависящего от времени Гамильтониана Аронова-Бома допускает непрерывное семейство различных
динамик, включая динамики, которые вытекают из критерия Паули для ротационной инвариантности, критерия Аронова-Бома для однозначности
и варианта критерия Паули, соответствующего цилиндрической симметрии, предложенной Хеннебергером. Зависящий от времени потокF(t), сваязывающий соленоид Аронова-Бома, приводит к зависящему от времени Гамильтониану Аронова-Бома. Точные решения в случае
наличия и в случае отсутствия недоступных областей для заряженных частиц исключают возможность применения обоих вариантов
критерия Паули. Решения содержат один зависящий от времени параметр α, целые значения которого соответствуют однозначным волновым
функциям. Допускается любое вещественное (целое или не целое) значение параметра α. Плотности заряда и тока зависят от α иF(t) только через комбинацию α−eF(t)/2π. Этот результат приводит к выводу, что физические эффекты изменения потока во время эксперимента могут бытя интерпретированы,
как локальные эффекты электрического поля, неизбежно связанные с изменяющимся магнитным потоком.
Il Nuovo Cimento A 04/1984; 79(4):391-409.
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ABSTRACT: We derive from a dynamical symmetry property that the linear and nonlinear Schrödinger equations with harmonic potential possess an infinite string of shape-preserving coherent wave-packet states with classical motion. Unlike the Schrödinger state with ΔxΔp=ℏ/2, the uncertainty product can be arbitrarily large for these states showing that classical motion is not necessarily linked with minimum uncertainty. We obtain a generalization of Sudarshan's diagonal coherent-state representation in terms of these states.
Phys. Rev. D. 06/1982; 25(12).
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ABSTRACT: We generalize the MacDowell-Martin bound on the slope parameterb
A for the spinless case to the case of spin-0-spin-1/2 elastic scattering with parity conservation. We give the optimal answer
for all energies as well as the simpler (slightly weaker) bound
cbA \geqslant \fracstot2 36psel [ Ö{1 + \frac9psel 4k2 stot2 } + 1 ] - \frac14k2 (k = c.m. momentum).cb^A \geqslant \frac{{\sigma _{tot}^2 }}{{36\pi \sigma _{el} }}\left[ {\sqrt {1 + \frac{{9\pi \sigma _{el} }}{{4k^2 \sigma _{tot}^2 }}} + 1} \right] - \frac{1}{{4k^2 }} (k = c.m. momentum).
Here the superscript A refers to the absorptive-part contribution. We also obtain unitarity restrictions on the helicity-flip
amplitude
cf + - A (t)/Ö{ - t} |t = 0cf_{ + - }^A (t)/\sqrt { - t} |_{t = 0}
in terms ofσ
tot,σ
el, andb
A(s).
Si generalizza il limite di McDowell- Martin sul parametro di inclinazioneb
A per il caso privo di spin fino al caso dello seattering elastico tra spin nullo e spin 1/2 con conservazione della parità.
Si dà una risposta ottimale per tutte le energie così come per il limite più semplice (leggermente più debole)
cbA \geqslant \fracstot2 36psel [ Ö{1 + \frac9psel 4k2 stot2 } + 1 ] - \frac14k2 (k = impulso del centro di massa).cb^A \geqslant \frac{{\sigma _{tot}^2 }}{{36\pi \sigma _{el} }}\left[ {\sqrt {1 + \frac{{9\pi \sigma _{el} }}{{4k^2 \sigma _{tot}^2 }}} + 1} \right] - \frac{1}{{4k^2 }}(k = impulso del centro di massa).
L'esponente A si riferisce al contributo della parte assorbente. Si ottengono restrizioni di unitarietà sull'ampiezza dell'elicità-flip
cf + - A (t)/Ö{ - t} |t = 0cf_{ + - }^A (t)/\sqrt { - t} |_{t = 0}
in termini diσ
tot,σ
el, eb
A(S).
Мы обобщаем гранипу МкДовелла-Мартина для параметра наклонаb
A для бесспинового случая на случай упругого рассеяния спина 0 на спине 1/2 с сохранением четности. Мы приводим онтимальный
ответ для всех энергий, а также более простую гранипу
cf + - A (t)/Ö{ - t} |t = 0cf_{ + - }^A (t)/\sqrt { - t} |_{t = 0}
в терминахσ
полн,σ
упр иb
A(S).
Il Nuovo Cimento A 03/1979; 50(3):443-455.
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S. M. Roy, G. Wanders
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ABSTRACT: Analyticity properties of pion-pion partial wave amplitudes are derived from the simplest crossing symmetric dispersion relations. A sizeable domain of analyticity is obtained; at each of its points the amplitudes can be computed in terms of physical quantities. Work supported by the Swiss National Science Foundation.
Physics Letters B - PHYS LETT B. 01/1978; 74:347-349.
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ABSTRACT: We derive upper and lower bounds on the imaginary part of the elastic scattering amplitude of two spinless particles in the physical region, in terms of the elastic cross section σel and the total cross section σtot, using unitarity alone. The bounds derived are the best possible ones, given only the stated unitarity constraints. The upper bound for high energies and small values of the momentum transfer squared t has a particularly simple and "universal" form, ImF(s, t)/ImF(s, 0)<~1-1/9ρ+3/8(ρ/9)2-(21/320)(ρ/9)3+⋯ if 2.5>~ρ≡(-t/4π)σtot2(s)/σel(s), which depends on the particular scattering process and on the energy and momentum transfer only through the dimensionless parameter ρ. We give explicit formulas and numerical values for the upper bound up to ρ=8.42. We compare the experimental curve of (dσ/dt)/(dσ/dt)t=0 versus 4(-t)(dσ/dt)t=0/σel with the theoretical upper bound on [ImF(s, t)/ImF(s, t=0)]]2 versus ρ. The quantities plotted in the experimental and theoretical curves are the same if the unpolarized cross sections are spin-independent and purely absorptive in the diffraction-peak region. We find that the experimental points for pp, p̅ p, π+p, and π-p scattering in the lab momentum range 6-13 GeV/c fall on a curve lying only slightly below the theoretical upper-bound curve, the difference being less than 10% for ρ in the range (0,3) and less than 25% for ρ in the range (3,5). We further notice that this experimental curve is universal. We also derive unitarity lower bounds on the nth derivatives of the absorptive part at t=0, and on the absorptive part for positive values of t within the Lehmann-Martin ellipse, in terms of σel and σtot. The corresponding bounds if σtot alone is known are also derived.
Phys. Rev. D. 04/1970; 1(9).
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ABSTRACT: We formulate hidden variable theories obeying the local causality condition of absence of faster than light signals, a condition weaker than the Einstein-Bell locality condition. We propose experimental tests of such theories and show that quantum mechanics can be embedded in them.
Physics Letters A.
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ABSTRACT: We present a set of closed systems of partial-wave equations for pion-pion scattering valid for −28 mπ2 ⩽ s ⩽ 125.31 mπ2. These equations give the real part of a given partial-wave amplitude in terms of scattering lengths and a convergent series of integrals over the physical values of the absorptive parts of all partial waves. Our equations are extensions of relations previously derived from fixed-t dispersion relations. The new equations are rigorous consequences of axiomatic analyticity and three channel crossing symmetry. As an application, the effect of the f0-meson on the I = O S-wave is evaluated.
Nuclear Physics B.
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ABSTRACT: If a classical Nambu-Goto string in D dimensions is required to have Poincaré invariance in d dimensions, d<D, then new boundary conditions involving free parameters whose numbers depend on D-d are allowed. We quantize these new string theories and show that the restricted Poincaré invariance still requires D=26. However, it allows choices of free parameters such that tachyons can be eliminated from the mass spectrum if d<~10. The new boundary conditions imply generalized Fubini-Veneziano commutation rules.
Phys. Rev. D. 33(12).
