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The trace anomaly and the cosmological constant problem are two typical breakdowns when applying the quantum principle to a general covariant or gravitational system. A quantum theory of spacetime reference frame is proposed and reviewed.…
Running couplings can be understood as arising from the spontaneous breaking of an exact scale invariance in appropriate effective theories with no dilatation anomaly. Any ordinary quantum field theory, even if it has massive fields, can be…
We study gravity coupled to a cosmological constant and a scale but not conformally invariant sector. In Minkowski vacuum, scale invariance is spontaneously broken. We consider small fluctuations around the Minkowski vacuum. At the…
The question of building a local diff-invariant effective gravitational action for the trace anomaly is reconsidered. General Relativity (GR) combined with the existing action for the trace anomaly is an inconsistent low energy effective…
New equations governing the scale transformation behaviors of a QFT with underlying structures are derived. These equations, with their several equivalent versions, can yield some new and significant insights and results that are difficult…
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…
The trace anomaly of quantum fields in electromagnetic or gravitational backgrounds implies the existence of massless scalar poles in physical amplitudes involving the stress-energy tensor. Considering first the axial anomaly and using QED…
We re-consider the quantum mechanics of scale invariant potentials in two dimensions. The breaking of scale invariance by quantum effects is analyzed by the explicit evaluation of the phase shift and the self-adjoint extension method. We…
Recent work has shown that complex quantum field theory emerges as a statistical mechanical approximation to an underlying noncommutative operator dynamics based on a total trace action. In this dynamics, scale invariance of the trace…
Within the framework of the recently proposed Taylor-Lagrange regularization scheme - which leads to finite elementary amplitudes in $4$-dimensional space-time with no additional dimensionful scales - we show that the trace of the…
The structure of the commutator algebra for conformal quantum mechanics is considered. Specifically, it is shown that the emergence of a dimensional scale by renormalization implies the existence of an anomaly or quantum-mechanical symmetry…
We propose that the consistent field renormalization of gravity requires a specific Weyl transformation of the metric tensor. As a consequence, proper length and time, as well as energy and momentum, become functions of scale. We estimate…
We generalize the scale invariant gravity by allowing a negative kinetic energy term for the classical scalar field. This gives birth to a new scalar-tensor theory of gravity, in which the scalar field is in fact an auxiliary field. For a…
We discuss for some particular non supersymmetric theories a generalized symmetry that includes both the scale and axial transformations and leads to a single current that may contain also a pseudoscalar term. The method, inspired by the…
In Quantum Field Theory models with spontaneously broken gauge invariance, renormalizability limits to four the degree of the Higgs potential, whose minima determine the vacuum state at tree-level. In many models, this bound has the…
A number of physical systems exhibit a particular form of asymptotic conformal invariance: within a particular range of distances, they are characterized by a long-range conformal interaction (inverse square potential), the absence of…
We examine the question of scale versus conformal invariance on maximally symmetric curved backgrounds and study general 2-derivative conformally invariant free theories of vectors and tensors. For spacetime dimension $D>4$, these conformal…
We consider the trace anomaly, which results from the integration of the massless conformal fermion field with the background of metric and antisymmetric tensor fields. The non-local terms in the anomaly-induced effective action do not…
The low energy effective action of gravity in any even dimension generally acquires non-local terms associated with the trace anomaly, generated by the quantum fluctuations of massless fields. The local auxiliary field description of this…
As applied to quantum theories, the program of renormalization is successful for `renormalizable models' but fails for `nonrenormalizable models'. After some conceptual discussion and analysis, an enhanced program of renormalization is…