1,981 research outputs found
Single-Valued Hamiltonian via Legendre-Fenchel Transformation and Time Translation Symmetry
Under conventional Legendre transformation, systems with a non-convex
Lagrangian will result in a multi-valued Hamiltonian as a function of conjugate
momentum. This causes problems such as non-unitary time evolution of quantum
state and non-determined motion of classical particles, and is physically
unacceptable. In this work, we propose a new construction of single-valued
Hamiltonian by applying Legendre-Fenchel transformation, which is a
mathematically rigorous generalization of conventional Legendre transformation,
valid for non-convex Lagrangian systems, but not yet widely known to the
physics community. With the new single-valued Hamiltonian, we study spontaneous
breaking of time translation symmetry and derive its vacuum state. Applications
to theories of cosmology and gravitation are discussed.Comment: Journal Version, 16pp. All results + conclusions un-changed, only
minor refinements to clarify the importance of our new LFT method and its
physics applications; references adde
Time-dependent Aharonov-Bohm effect on the noncommutative space
We study the time-dependent Aharonov-Bohm effect on the noncommutative space.
Because there is no net Aharonov-Bohm phase shift in the time-dependent case on
the commutative space, therefore, a tiny deviation from zero indicates new
physics. Based on the Seiberg-Witten map we obtain the gauge invariant and
Lorentz covariant Aharonov-Bohm phase shift in general case on noncommutative
space. We find there are two kinds of contribution: momentum-dependent and
momentum-independent corrections. For the momentum-dependent correction, there
is a cancellation between the magnetic and electric phase shifts, just like the
case on the commutative space. However, there is a non-trivial contribution in
the momentum-independent correction. This is true for both the time-independent
and time-dependent Aharonov-Bohm effects on the noncommutative space. However,
for the time-dependent Aharonov-Bohm effect, there is no overwhelming
background which exists in the time-independent Aharonov-Bohm effect on both
commutative and noncommutative space. Therefore, the time-dependent
Aharonov-Bohm can be sensitive to the spatial noncommutativity. \draftnote{The
net correction is proportional to the product of the magnetic fluxes through
the fundamental area represented by the noncommutative parameter , and
through the surface enclosed by the trajectory of charged particle.} More
interestingly, there is an anti-collinear relation between the logarithms of
the magnetic field and the averaged flux (N is the number of
fringes shifted). This nontrivial relation can also provide a way to test the
spatial noncommutativity. For , our estimation on the
experimental sensitivity shows that it can reach the scale. This
sensitivity can be enhanced by using stronger magnetic field strength, larger
magnetic flux, as well as higher experimental precision on the phase shift.Comment: 12 pages, 1 figure; v2, accepted version by PL
RESEARCH ON THE EMBODIMENT OF SINO AMERICAN ELEMENTS IN MODERN ADVERTISING DESIGN AND THE IMPACT OF ALLEVIATING AUDIENCE PSYCHOLOGICAL ANXIETY
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