39 research outputs found
Relativistic spin operator and Lorentz transformation of spin state of a massive Dirac particle
We have shown the covariant relativistic spin operator is equivalent to the
spin operator commuting with the free Dirac Hamiltonian. This implies that the
covariant relativistic spin operator is a good quantum observable. The
covariant relativistic spin operator has the pure quantum contribution which
does not exist in the classical covariant spin operator. Based on this
equivalence reduced spin states can be claerly defined. We have shown the
change in the entropy of a reduced spin density matrix sweeps through the whole
range according to the relative motion of an observer.Comment: published versio
Newton-Wigner position operator and its corresponding spin operator in relativistic quantum mechanics
A relativistic spin operator is to be the difference between the total and
orbital angular momentum. As the unique position operator for a localized
state, the remarkable Newton-Wigner position operator, which has all desirable
commutation relations as a position operator, can give a proper spin operator.
Historically important three spin operators respectively proposed by Bogolubov
et al., Pryce, and Foldy-Woutheysen are investigated to manifest a
corresponding spin operator to the Newton-Wigner position operator. We clarify
a unique spin operator in relativistic quantum mechanics described by the Dirac
Hamiltonian
Quantum Probability assignment limited by relativistic causality
The quantum nonlocality is limited by relativistic causality, however, the
reason is not fully understood yet. The relativistic causality condition on
nonlocal correlations has been usually accepted as a prohibition of
faster-than-light signaling, called no-signaling condition. We propose another
causality condition from the observation that space-like separate events should
have no causal relationship. It is proved that the new condition is stronger
than no-signaling condition for a pair of binary devices. We derive the
standard probability assignment rule, so-called Born rule, on quantum
measurement, which determines the degree of quantum nonlocality, by using
relativistic causality constraint. This shows how the causality limits the
upper bound of quantum nonlocality through quantum probability assignment.Comment: We separated out the first (main part) of the version 1 and made more
clear and detailed analysis to prove our arguments on the relation between
quantum physics and relativit
Spin Operators for Massive Particles
Since the discovery a century ago, spin describing the intrinsic angular
momentum of massive elementary particles has exposed its nature and significant
roles in wide ranges of (relativistic) quantum phenomena and practical
applications for future quantum technology. Emerging inconsistencies have also
disclosed its telltale incomplete description. Finding relativistic spins
(operators) of massive particles is a long-standing fundamental problem from
the beginning of relativistic quantum mechanics. Here we present the rigorous
derivation and the representation of spin operators from the spacetime
symmetry. The covariant parity operation, defined by the spin operators,
naturally leads to a fundamental equation equivalent to the covariant Dirac
equation, which manifests existent relativistic spins. Proper understanding
position operator in the Dirac theory on account of the spin operator through
total angular momentum predicts no Zitterbewegung as well as conserving orbital
and spin currents. The spin operators can be applicable for unraveling the
inconsistencies and for exploring unveiled physics of massive particles.Comment: new result for Zitterbewegung added and conserved spin current
modified, the main body refine
Relativistic Spin and Dirac Spin in relativistically covariant Stern-Gerlach Experiment
We have studied a relativistically covariant Stern-Gerlach (SG) experiment
for a relativistic spin and a Dirac spin. We have obtained the relativistic
spin in an arbitrary frame by using the classical spin dipole tensor, which
gives the covariant spin dipole interactions, and the relation between a spin
and a spin magnetic dipole moment. The relativistic spin is shown to have
problems to become a proper spin operator for a massive relativistic particle
because of two reasons. First, the relativistic spin three-vector operators
cannot satisfy the spin algebra. Second, the SG experiment for the relativistic
particle provides a paradox between two observers in the particle rest frame
and the laboratory frame, in which the particle is moving. We have shown that
the paradox in the SG experiment is resolved by the Dirac spin, which is
covariantly defined by a Lorentz transformation in the Dirac spinor
representation. The Dirac spin three-vector operators satisfy the spin algebra.
It is shown that the SG experiment for the Dirac spin in the inertial frame,
where there is only magnetic field, can determine the spin without the
information of the momentum of the particle.
This shows that the reduced spin density matrix for the Dirac particle can be
well-defined by integrating out the momentum degrees of freedom
Spin operators and representations of the Poincar\'e group
We present the rigorous derivation of covariant spin operators from a general
linear combination of the components of the Pauli-Lubanski vector. It is shown
that only two spin operators satisfy the spin algebra and transform properly
under the Lorentz transformation, which admit the two inequivalent
finite-dimensional representations for the Lorentz generators through the
complexification of the group. In case that the Poincar\'e group is
extended by parity operation, the spin operator in the direct sum
representation of the two inequivalent representations, called the new spin
distinguished from the Dirac spin, is shown to be equivalent to axial and
Hermitian spin operators for particle and antiparticle. We have shown that for
spin , the Noether conserved current for a rotation can be divided into
separately conserved orbital and spin part for the new spin, unlike for the
Dirac spin. This implies that the new spin not the Dirac spin provides good
quantum observables.Comment: We clarified some more mathematical subtleties, add comments, and
correct typo
Limits on Quantum Probability Rule by no-Signaling Principle
We have studied the possibility of post-quantum theories more nonlocal than
the (standard) quantum theory using the modification of the quantum probability
rule under the no-signaling condition. For this purpose we have considered the
situation that two spacelike separate parties Alice and Bob share an entangled
two qubit system. We have modified the quantum probability rule as small as
possible such that the first local measurements are governed by the usual Born
rule and the second measurement by the modified quantum probability rule. We
have shown that only the maximally entangled states can have higher nonlocality
than the quantum upper bound while satisfying the no-signaling condition. This
fact could be a partial explanation for why the nonlocality of the quantum
theory is limited. As a by-product we have found the systematic way to obtain a
variety of nonlocal boxes
Proper relativistic position operators in 1+1 and 2+1 dimensions
We have revisited the Dirac theory in 1+1 and 2+1 dimensions by using the
covariant representation of the parity-extended Poincar\'e group in their
native dimensions. The parity operator plays a crucial role in deriving wave
equations in both theories. We studied two position operators, a canonical one
and a covariant one that becomes the particle position operator projected onto
the particle subspace. In 1+1 dimensions the particle position operator, not
the canonical position operator, provides the conserved Lorentz generator. The
mass moment defined by the canonical position operator needs an additional
unphysical spin-like operator to become the conserved Lorentz generator in 1+1
dimensions. In 2+1 dimensions, the sum of the orbital angular momentum given by
the canonical position operator and the spin angular momentum becomes a
constant of motion. However, orbital and spin angular momentum do not conserve
separately. On the other hand the orbital angular momentum given by the
particle position operator and its corresponding spin angular momentum become a
constant of motion separately.Comment: 9 page
Mean spin entanglement of two massive Dirac particles under Lorentz transformations
We have studied the relativistic effects on the mean spin entanglement of two
massive Dirac particles using the simultaneous eigen-spinors of the
Foldy-Woutheysen mean spin operator and the Dirac Hamiltonian. We have obtained
the transformation matrix from the spinor with specific momentum to the spinor
with a transformed momentum under an arbitrary Lorentz transformation. Using
the transformation matrix we have shown the consistent monotonic behavior
between the concurrence and the maximum value of Bell parameter in Bell
inequality of transformed spin states
Entanglement of thermal scalar fields in a compact space space
Using the thermal Green's function approach we propose a general method to
investigate entanglement of the vacuum state or thermal ground states in an
arbitrary dimensional space-time. As an application we show quantum
separability of the massive thermal scalar field vacuum in the 1+1 dimensional
cylindrical space-time. Separability is demonstrated using the positive partial
transpose criterion for effective two-mode Gaussian states of collective
operators. In this case, for all mass and temperature values entanglement is
absent between the collective operators.Comment: title change