相关论文: The Dimensional-Reduction Anomaly in Spherically S…

In a wide class of D-dimensional spacetimes which are direct or semi-direct sums of a (D-n)-dimensional space and an n-dimensional homogeneous ``internal'' space, a field can be decomposed into modes. As a result of this mode decomposition,…

D-theory is an alternative non-perturbative approach to quantum field theory formulated in terms of discrete quantized variables instead of classical fields. Classical scalar fields are replaced by generalized quantum spins and classical…

If we restrict a quantum field defined on a regular D dimensional curved manifold to a d dimensional submanifold then the resulting field will still have the singularity of the original D dimensional model. We show that a singular…

We first briefly review some aspects of the techniques of dealing with ultraviolet divergences in Feynman amplitudes in an Euclidian $D$-dimensional space-time. Next we consider compactification of a $d$-dimensional ($d\leq D$) subspace.…

Hints from a number of different approaches to quantum gravity point to a phenomenon of "spontaneous dimensional reduction" to two spacetime dimensions near the Planck scale. I examine the physical meaning of the term "dimension" in this…

Renormalization factors are most easily extracted by going to the massless limit of the quantum field theory and retaining only a single momentum scale. We derive factors and renormalized Green functions to all orders in perturbation theory…

A series of old and recent theoretical observations suggests that the quantization of gravity would be feasible, and some problems of Quantum Field Theory would go away if, somehow, the spacetime would undergo a dimensional reduction at…

If gravity is asymptotically safe, operators will exhibit anomalous scaling at the ultraviolet fixed point in a way that makes the theory effectively two-dimensional. A number of independent lines of evidence, based on different approaches…

One-dimensional quantum optical models usually rest on the intuition of large scale separation or frozen dynamics associated with the different spatial dimensions, for example when studying quasi one-dimensional atomic dynamics, potentially…

We discuss some problems related to dimensional reductions of gravity theories to two-dimensional and one-dimensional dilaton gravity models. We first consider the most general cylindrical reductions of the four-dimensional gravity and…

It is shown that the local coupling of a higher dimensional graviton to a closed degenerate two-form produces dimensional reduction by spontaneous breakdown of extra-dimensional translational symmetry. Four dimensional Poincar\'e invariance…

A number of very different approaches to quantum gravity contain a common thread, a hint that spacetime at very short distances becomes effectively two dimensional. I review this evidence, starting with a discussion of the physical meaning…

It is shown that regularisation by dimensional reduction is a viable alternative to dimensional regularisation in non-supersymmetric theories.

Over the past few years, evidence has begun to accumulate suggesting that spacetime may undergo a "spontaneous dimensional reduction" to two dimensions near the Planck scale. I review some of this evidence, and discuss the (still very…

Many theories of quantum gravity live in higher dimensions, and their reduction to four dimensions via mechanisms such as Kaluza-Klein compactification or brane world models have associated problems. We propose a novel mechanism of…

Reduction from a higher-dimensional to a lower-dimensional field theory can display special features when the zero-level ground state has nontrivial dependence on the reduction coordinates. In particular, a delayed `covert' form of…

This is the first in a series of papers addressing the phenomenon of dimensional transmutation in nonrelativistic quantum mechanics within the framework of dimensional regularization. Scale-invariant potentials are identified and their…

Results from a number of different approaches to quantum gravity suggest that the effective dimension of spacetime may drop to $d=2$ at small scales. I show that two different dimensional estimators in causal set theory display the same…

The quantum-mechanical D-dimensional inverse square potential is analyzed using field-theoretic renormalization techniques. A solution is presented for both the bound-state and scattering sectors of the theory using cutoff and dimensional…

A ten-dimensional supersymmetric gauge theory is written in terms of N=1, D=4 superfields. The theory is dimensionally reduced over six-dimensional coset spaces. We find that the resulting four-dimensional theory is either a softly broken…