1,959 research outputs found
Homotopy approach to quantum gravity
I construct a finite-dimensional quantum theory from general relativity by a
homotopy method. Its quantum history is made up of at least two levels of
fermionic elements. Its unitary group has the diffeomorphism group as singular
limit. Its gravitational metrical form is the algebraic square. Its spinors are
multivectors.Comment: For International Journal of Theoretical Physics, Oberwolfach 2006
issu
Nature as quantum computer
Set theory reduces all processes to assembly and disassembly. A similar
architecture is proposed for nature as quantum computer. It resolves the
classical space-time underlying Feynman diagrams into a quantum network of
creation and annihilation processes, reducing kinematics to quantum statistics,
and regularizing the Lie algebra of the Einstein diffeomorphism group. The
usually separate and singular Lie algebras of kinematics, statistics, and
conserved currents merge into one regular statistics Lie algebra.Comment: 16 pages. Paper contributed to a memorial volume for Jack Schwartz
edited by E. Schonber
MELENCOLIA I: The physics of Albrecht Duerer
Duerer's engraving ``MELENCOLIA I'' was circulated in two versions not
previously distinguished. Besides their conspicuous early Renaissance
scientific instruments and tools, they contain numerous apparently unreported
concealments whose detection reveals heresies expressed in the work. The main
one is encoded in the motto {\em MELENCOLIA I} itself: Natural Philosophy, not
Mathematical Philosophy or Theological Philosophy, is the way to knowledge.
Unusual optical illusions and subliminal images, differing between the two
versions, declare the relativity and ambiguity of perception, and indicate that
the work was a Humanist document intended for a Humanist viewership.Comment: 38 pages. Corrects and extends an earlier versio
Quantum field theory in quantum set algebra
A modular quantum architecture is given for the space-time, particles, and
fields of the Standard Model and General Relativity. It assumes a right-handed
neutrino, so that based on their multiplet structure all fundamental fermions
have isospin 1/2. This opens the possibility that the Higgs field can be
identified with the Yang -field of 1947. The quantum gravitational metric
form proposed is a quantification of the Killing form of the quantum space-time
cell. There is no trace of the black hole phenomenon at the one-cell quantum
level.Comment: 19 page
General quantization
Segal's hypothesis that physical theories drift toward simple groups follows
from a general quantum principle and suggests a general quantization process. I
general-quantize the scalar meson field in Minkowski space-time to illustrate
the process. The result is a finite quantum field theory over a finite quantum
space-time with higher symmetry than the singular theory. Multiple
quantification connects the levels of the theory.Comment: 25 pages. Edited to 21 pages. References added. Typos remove
Palev Statistics and the Chronon
A finite relativistic quantum space-time is constructed. Its unit cell has
Palev statistics defined by a spin representation of an orthogonal group. When
the Standard Model and general relativity are physically regularized by such
space-time quantization, their gauges are fixed by nature; the cell groups
remain.Comment: 14 pages. For the proceedings of IX International Workshop on Lie
Theory and its Applications in Physics. Bulgarian Academy of Sciences 2011.
Ed. V. K. Dobre
Interpretation of the topological terms in gauge system
We provide an alternative interpretation for the topological terms in physics
by investigating the low-energy gauge interacting system. The asymptotic
behavior of the gauge field at infinity indicates that it traces out a closed
loop in the infinite time interval: -infinity, + infinity. Adopting Berry's
argument of geometric phase, we show that the adiabatic evolution of the gauge
system around the loop results in an additional term to the effective action:
the Chern-Simons term for three-dimensional spacetime, and the Pontrjagin term
for the four-dimensional spacetime.Comment: 12 pages, RevTeX; submitted to Phys. Rev. Let
Quantum-Statistical Computation
Systems of spin 1, such as triplet pairs of spin-1/2 fermions (like
orthohydrogen nuclei) make useful three-terminal elements for quantum
computation, and when interconnected by qubit equality relations are universal
for quantum computation. This is an instance of quantum-statistical
computation: some of the logical relations of the problem are satisfied
identically in virtue of quantum statistics, which takes no time. We show
heuristically that quantum-statistical ground-mode computation is substantially
faster than pure ground-mode computation when the ground mode is reached by
annealing.Comment: 12 pages, LaTeX Minor changes for journa
Quantum ground-state computation with static gates
We develop a computation model for solving Boolean networks that implements
wires through quantum ground-state computation and implements gates through
identities following from angular momentum algebra and statistics. The gates
are static in the sense that they contribute Hamiltonian 0 and hold as
constants of the motion; only the wires are dynamic. Just as a spin 1/2 makes
an ideal 1-bit memory element, a spin 1 makes an ideal 3-bit gate. Such gates
cost no computation time: relaxing the wires alone solves the network. We
compare computation time with that of an easier Boolean network where all the
gate constraints are simply removed. This computation model is robust with
respect to decoherence and yields a generalized quantum speed-up for all NP
problems.Comment: 10 pages, LaTeX, 1 PS figur
Finite Quantum Kinematics of the Harmonic Oscillator
Arbitrarily small changes in the commutation relations suffice to transform
the usual singular quantum theories into regular quantum theories. This process
is an extension of canonical quantization that we call general quantization.
Here we apply general quantization to the time-independent linear harmonic
oscillator. The unstable Heisenberg group becomes the stable group SO(3). This
freezes out the zero-point energy of very soft or very hard oscillators, like
those responsible for the infrared or ultraviolet divergencies of usual field
theories, without much changing the medium oscillators. It produces pronounced
violations of equipartition and of the usual uncertainty relations for soft or
hard oscillators,and interactions between the previously uncoupled excitation
quanta of the oscillator, weakly attractive for medium quanta, strongly
repulsive for soft or hard quanta.Comment: Based on Ph.D. thesis of Mohsen Shiri-Garakan
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