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We continue ongoing research work on applying the homological algebraic conceptual and technical machinery of Abstract Differential Geometry towards formulating a finitary, causal and quantal version of vacuum Einstein Lorentzian gravity…
We examine the weak-field, zero-coupling limit of Yang--Mills gravity as recently formulated by Partanen and Tulkki, viewed as a free quantum field theory. In this approximation the theory has a ghostly teleparallel vacuum. We suggest that…
New quantum modes of the free scalar field are derived in a special time-evolution picture that may be introduced in moving charts of de Sitter backgrounds. The wave functions of these new modes are solutions of the Klein-Gordon equation…
The perturbative dynamics of quantum field theories is described by a recursive expansion similar to the well known loop expansion. The equivalent formulation based on low-energy dynamics via an expansion in derivatives is well known in the…
We give a gauge-invariant description of the dual superconductivity for deriving quark confinement and mass gap in Yang-Mills theory.
We examine in non-Abelian gauge theory the heavy quark limit in the presence of the (anti-)self-dual homogeneous background field and see that a confining potential emerges, consistent with the Wilson criterion, although the potential is…
We discuss a unified model of quark confinement and new cosmic expansion with linear potentials based on a general $(SU_3)_{color} \times (U_1)_{baryon}$ symmetry. The phase functions in the usual gauge transformations are generalized to…
A gauge-invariant wavefunctional is proposed as an approximation to the ground state of Yang-Mills theory in 2+1 dimensions, quantized in temporal gauge. The proposed vacuum state is the true ground state of the appropriate Hamiltonian in…
We investigate the temporal Wilson loop using the Hamiltonian approach to Yang-Mills theory. In simple cases such as the Abelian theory or the non-Abelian theory in (1+1) dimensions, the known results can be reproduced using unitary…
Three-dimensional Yang-Mills theory is investigated in the Hamiltonian formalism based on the Karabali-Nair variable. A new algorithm is developed to obtain the renormalized Hamiltonian by identifying local counterterms in Lagrangian with…
A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific…
We present a family of nonrelativistic Yang-Mills gauge theories in D+1 dimensions whose free-field limit exhibits quantum critical behavior with gapless excitations and dynamical critical exponent z=2. The ground state wavefunction is…
In the present article we display a new constructive quantum field theory approach to quantum gauge field theory, utilizing the recent progress in the integration theory on the moduli space of generalized connections modulo gauge…
A systematic study of the Weyl-type / Yang-Mills-type action possessing local conformal invariance and quadratic curvature is undertaken. The dynamical breaking of this conformal invariance / scale invariance induces general relativity (GR)…
Quantum theory of the free Maxwell field in Minkowski space is constructed using a representation in which the self dual connection is diagonal. Quantum states are now holomorphic functionals of self dual connections and a decomposition of…
This article reports an explicit function form for confining classical Yang-Mills vector potentials and quantum fluctuations around the classical field. The classical vector potential, which is composed of a confining localized function and…
We show how to use quantum mechanics on the group manifold U(N) as a tool for problems in U(N) representation theory. The quantum mechanics reduces to free fermions on the circle, which in the large N limit become relativistic. The theory…
In this work we discuss an analytic approach towards the solution of pure Yang-Mills theory in 3+1 dimensional spacetime which strongly suggests that the recent strategy already applied to pure Yang-Mills theory in 2+1 can be extended to…
Using closed positive extensions of the quadratic form in the potential term we provide alternative solutions to the eigenstate equation for the free quantum field Hamiltonian in the Schr\"o\-din\-ger representation. We show that admissible…
Using Hamilton-Jacobi formalism we investigated the massive Yang-Mills theory on both extended and reduced phase-space. The integrability conditions were discussed and the actions were calculated.