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Search Results: 1 - 10 of 14815 matches for " Christian Wiesendanger "
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Conservation of Gravitational Energy-Momentum and Inner Diffeomorphism Group Gauge Invariance  [PDF]
Christian Wiesendanger
Journal of Modern Physics (JMP) , 2013, DOI: 10.4236/jmp.2013.48A006
Abstract:

Viewing gravitational energy momentum \"\" as equal by observation, but different in essence from inertial energy-momentum \"\" requires two different symmetries to account for their independent conservations—spacetime and inner translation invariance. Gauging the latter a generalization of non-Abelian gauge theories of compact Lie groups is developed resulting in the gauge theory of the non-compact group of volume-preserving diffeomorphisms of an inner Minkowski space M4. As usual the gauging requires the introduction of a covariant derivative, a gauge field and a field strength operator. An invariant and minimal gauge field Lagrangian is derived. The classical field dynamics and the conservation laws for the new gauge theory are developed. Finally, the theorys Hamiltonian in the axial gauge is expressed by two times six unconstrained independent canonical variables obeying the usual Poisson brackets and the positivity of the Hamiltonian is related to a condition on the support of the gauge fields.

Conservation of Gravitational Energy Momentum and Renormalizable Quantum Theory of Gravitation  [PDF]
Christian Wiesendanger
Journal of Modern Physics (JMP) , 2013, DOI: 10.4236/jmp.2013.48A013
Abstract:

Viewing gravitational energy-momentum as equal by observation, but different in essence from inertial energymomentum \"\" naturally leads to the gauge theory of volume-preserving diffeomorphisms of an inner Minkowski space \"\" which can describe gravitation at the classical level. This theory is quantized in the path integral formalism starting with a non-covariant Hamiltonian formulation with unconstrained canonical field variables and a manifestly positive Hamiltonian. The relevant path integral measure and weight are then brought into a Lorentz- and gauge-covariant form allowing to express correlation functions—applying the De Witt-Faddeev-Popov approach—in any meaningful gauge. Next the Feynman rules are developed and the quantum effective action at one loop in a background field approach is renormalized which results in an asymptotically free theory without presence of other fields and in a theory without asymptotic freedom including the Standard Model (SM) fields. Finally the BRST apparatus is developed as preparation for the renormalizability proof to all orders and a sketch of this proof is given.

General Relativity as the Classical Limit of the Renormalizable Gauge Theory of Volume Preserving Diffeomorphisms  [PDF]
Christian Wiesendanger
Journal of Modern Physics (JMP) , 2014, DOI: 10.4236/jmp.2014.510098
Abstract:

The different roles and natures of spacetime appearing in a quantum field theory and in classical physics are analyzed implying that a quantum theory of gravitation is not necessarily a quantum theory of curved spacetime. Developing an alternative approach to quantum gravity starts with the postulate that inertial energy-momentum and gravitational energy-momentum need not be the same for virtual quantum states. Separating their roles naturally leads to the quantum gauge field theory of volume-preserving diffeomorphisms of an inner four-dimensional space. The classical limit of this theory coupled to a quantized scalar field is derived for an on-shell particle where inertial energy-momentum and gravitational energy-momentum coincide. In that process the symmetry under volume-preserving diffeomorphisms disappears and a new symmetry group emerges: the group of coordinate transformations of four-dimensional spacetime and with it General Relativity coupled to a classical relativistic point particle.

A Renormalizable Theory of Quantum Gravity: Renormalization Proof of the Gauge Theory of Volume Preserving Diffeomorphisms  [PDF]
Christian Wiesendanger
Journal of Modern Physics (JMP) , 2014, DOI: 10.4236/jmp.2014.510099
Abstract:

Inertial and gravitational mass or energy momentum need not be the same for virtual quantum states. Separating their roles naturally leads to the gauge theory of volume-preserving diffeomorphisms of an inner four-dimensional space. The gauge-fixed action and the path integral measure occurring in the generating functional for the quantum Green functions of the theory are shown to obey a BRST-type symmetry. The related Zinn-Justin-type equation restricting the corresponding quantum effective action is established. This equation limits the infinite parts of the quantum effective action to have the same form as the gauge-fixed Lagrangian of the theory proving its spacetime renormalizability. The inner space integrals occurring in the quantum effective action which are divergent due to the gauge group’s infinite volume are shown to be regularizable in a way consistent with the symmetries of the theory demonstrating as a byproduct that viable quantum gauge field theories are not limited to finite-dimensional compact gauge groups as is commonly assumed.

Scattering Cross-Sections in Quantum Gravity—The Case of Matter-Matter Scattering  [PDF]
Christian Wiesendanger
Journal of Modern Physics (JMP) , 2015, DOI: 10.4236/jmp.2015.63032
Abstract: Viewing gravitational energy-momentum PGμ as equal by observation, but different in essence from inertial energy-momentum PIμ naturally leads to the gauge theory of volume-preserving diffeomorphisms of a four-dimensional inner space. To analyse scattering in this theory, the gauge field is coupled to two Dirac fields with different masses. Based on a generalized LSZ reduction formula the S-matrix element for scattering of two Dirac particles in the gravitational limit and the corresponding scattering cross-section are calculated to leading order in perturbation theory. Taking the non-relativistic limit for one of the initial particles in the rest frame of the other the Rutherford-like cross-section of a non-relativistic particle scattering off an infinitely heavy scatterer calculated quantum mechanically in Newtonian gravity is recovered. This provides a non-trivial test of the gauge field theory of volume-preserving diffeomorphisms as a quantum theory of gravity.
Isometrodynamics and Gravity
Christian Wiesendanger
Physics , 2009,
Abstract: Isometrodynamics (ID), the gauge theory of the group of volume-preserving diffeomorphisms of an "inner" D-dimensional flat space, is tentatively interpreted as a fundamental theory of gravity. Dimensional analysis shows that the Planck length l_P - and through it \hbar and \Gamma - enters the gauge field action linking ID and gravity in a natural way. Noting that the ID gauge field couples solely through derivatives acting on "inner" space variables all ID fields are Taylor-expanded in "inner" space. Integrating out the "inner" space variables yields an effective field theory for the coefficient fields with l_P^2 emerging as the expansion parameter. For \hbar goint to zero only the leading order field does not vanish. This classical field couples to the matter Noether currents and charges related to the translation invariance in "inner" space. A model coupling this leading order field to a matter point source is established and solved. Interpreting the matter Noether charge in terms of gravitational mass Newton's inverse square law is finally derived for a static gauge field source and a slowly moving test particle. Gravity emerges as potentially related to field variations over "inner" space and might microscopically be described by the ID gauge field or equivalently by an infinite string of coefficient fields only the leading term of which is related to the macroscopical effects of gravity.
Classical Isometrodynamics
Christian Wiesendanger
Physics , 2009, DOI: 10.1103/PhysRevD.80.025018
Abstract: A generalization of non-Abelian gauge theories of compact Lie groups is developed by gauging the non-compact group of volume-preserving diffeomorphisms of a $D$-dimensional space R^D. This group is represented on the space of fields defined on M^4 x R^D. As usual the gauging requires the introduction of a covariant derivative, a gauge field and a field strength operator. An invariant and minimal gauge field Lagrangian is derived. The classical field dynamics and the conservation laws of the new gauge theory are developed. Finally, the theory's Hamiltonian in the axial gauge and its Hamiltonian field dynamics are derived.
Quantum Isometrodynamics
Christian Wiesendanger
Physics , 2009, DOI: 10.1103/PhysRevD.80.025019
Abstract: Classical Isometrodynamics is quantized in the Euclidean plus axial gauge. The quantization is then generalized to a broad class of gauges and the generating functional for the Green functions of Quantum Isometrodynamics (QID) is derived. Feynman rules in covariant Euclidean gauges are determined and QID is shown to be renormalizable by power counting. Asymptotic states are discussed and new quantum numbers related to the "inner" degrees of freedom introduced. The one-loop effective action in a Euclidean background gauge is formally calculated and shown to be finite and gauge-invariant after renormalization and a consistent definition of the arising "inner" space momentum integrals. Pure QID is shown to be asymptotically free for all dimensions of "inner" space $D$ whereas QID coupled to the Standard Model fields is not asymptotically free for D <= 7. Finally nilpotent BRST transformations for Isometrodynamics are derived along with the BRST symmetry of the theory and a scetch of the general proof of renormalizability for QID is given.
Scattering Cross-Sections in Quantum Gravity - the Case of Matter-Matter Scattering
Christian Wiesendanger
Physics , 2012,
Abstract: Viewing gravitational energy-momentum as equal by observation, but different in essence from inertial energy-momentum naturally leads to the gauge theory of volume-preserving diffeormorphisms of a four-dimensional in- ner space. To analyse scattering in this theory the gauge field is coupled to two Dirac fields with different masses. Based on a generalized LSZ reduction formula the S-matrix element for scattering of two Dirac particles in the gravitational limit and the corresponding scattering cross-section are calculated to leading order in perturbation theory. Taking the non-relativistic limit for one of the initial particles in the rest frame of the other the Rutherford-like cross-section of a non-relativistic particle scattering off an infinitely heavy scatterer calculated quantum mechanically in Newtonian gravity is recovered. This provides a non-trivial test of the gauge field theory of volume-preserving diffeomorphisms as a quantum theory of gravity
Field-Dependent Size and Shape of Single Magnetic Skyrmions
Niklas Romming,André Kubetzka,Christian Hanneken,Kirsten von Bergmann,Roland Wiesendanger
Physics , 2015, DOI: 10.1103/PhysRevLett.114.177203
Abstract: The atomic-scale spin structure of individual isolated skyrmions in an ultrathin film is investigated in real space by spin-polarized scanning tunneling microscopy. Their axial symmetry as well as their unique rotational sense is revealed by using both out-of-plane and in-plane sensitive tips. The size and shape of skyrmions change as a function of magnetic field. An analytical expression for the description of skyrmions is proposed and applied to connect the experimental data to the original theoretical model describing chiral skyrmions. Thereby, the relevant material parameters responsible for skyrmion formation can be obtained.
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