Gravitational anomaly

In theoretical physics Theoretical physics attempts to understand the world by making a model of reality, used for rationalizing, explaining, and predicting physical phenomena through a "physical theory". There are three types of theories in physics: mainstream theories, proposed theories and fringe theories.

Some physical theories are backed by observation, whereas others are not.
..... Click the link for more information. , a gravitational anomaly is an example of an anomaly anomaly is a classical symmetry-i.e. a symmetry of the Lagrangian-that is broken by quantum effects, usually in quantum field theories. Anomalies in gauge theories have important connections to topology and geometry.

Although anomalies can be considered a short-distance, ultraviolet effect-because
..... Click the link for more information. : it is an effect of quantum mechanics Quantum mechanics is a fundamental physical theory which extends and corrects Newtonian mechanics, especially at the atomic and subatomic levels. It is the underlying framework of many fields of physics and chemistry, including condensed matter physics, quantum chemistry, and particle physics. The term quantum (Latin, "how much") refers to the discrete units that the theory assigns to certain physical quantities, such as the energy of an atom at rest (see Figure 1, at right).
..... Click the link for more information.  - usually a one-loop diagram - that invalidates the general covariance general covariance (also known as diffeomorphism invariance) is the invariance of physical laws (for example, the equations of general relativity) under arbitrary coordinate transformations. This means, for example, that such laws take the same mathematical form regardless of whether they are expressed in an accelerating or non-accelerating reference frame. Alternatively, one could say that a generally covariant theory is one which treats time-like and space-like coordinates in the same way.
..... Click the link for more information.  of a theory of general relativity General relativity (GR) or general relativity theory (GRT) is a fundamental physical theory of gravitation which corrects and extends Newtonian gravitation, especially at the macroscopic level of stars or planets.

General relativity may be regarded as an extension of special relativity, this latter theory correcting Newtonian mechanics at high velocities.
..... Click the link for more information.  combined with some other fields. The adjective "gravitational" is derived from the symmetry of a gravitational theory, namely from general covariance.

The anomaly usually appears as a Feynman diagram Feynman diagram is a bookkeeping device for performing calculations in quantum field theory, invented by American physicist Richard Feynman. They are sometimes also referred to as Stückelberg diagrams or (for a subset of special cases) penguin diagrams.

Motivation and history

The problem of calculating scattering cross sections in particle physics reduces to summing over the amplitudes of all possible intermediate states, in what is known as a perturbation expansion.
..... Click the link for more information.  with a chiral chiral if it is not identical to its mirror image (see Chirality (mathematics)). The spin of a particle may be used to define a handedness for that particle. A symmetry transformation between the two is called parity. The action of parity acting on a Dirac fermion is called chiral symmetry.
..... Click the link for more information.  fermion Fermions, named after Enrico Fermi, are particles which form totally-antisymmetric composite quantum states. As a result, they are subject to the Pauli exclusion principle and obey Fermi-Dirac statistics. The spin-statistics theorem states that fermions have half-integer spin. One possible way of visualizing spin is that particles with a 1/2 spin, i.e. fermions have to be rotated by two full rotations to return them to their initial state.
..... Click the link for more information.  running in the loop (a polygon) with n external gravitons graviton is a hypothetical elementary particle that transmits the force of gravity in most quantum gravity systems. In order to do this, one theory posits that gravitons have to be always-attractive (gravity never pushes), work over any distance (gravity is universal) and come in unlimited numbers (to provide high strengths near stars). In quantum theory, these requirements define an even-spin (spin 2 in this case) boson with a rest mass of zero.
..... Click the link for more information.  attached to the loop where where is the spacetime spacetime, in the theories of special relativity and general relativity, is time and three-dimensional space treated together as a single four-dimensional object. Spacetimes are the arenas in which all physical events take place — for example, the motion of planets around the Sun may be described in a particular type of spacetime, or the motion of light around a rotating star may be described in another type of spacetime.
..... Click the link for more information.  dimension. Anomalies only occur in even spacetime dimensions. General covariance is a very important symmetry for the consistency of the whole theory, and therefore all gravitational anomalies must cancel out.

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