Feynman slash notation

In the study of Dirac fields in quantum field theory, Richard Feynman invented the convenient Feynman slash notation (less commonly known as the Dirac slash notation). If A is a covariant vector (i.e., a 1-form),

using the Einstein summation notation where γ are the gamma matrices.

Identities

Using the anticommutators of the gamma matrices, one can show that for any and ,

where is the identity matrix in four dimensions. In particular,

Further identities can be read off directly from the gamma matrix identities by replacing the metric tensor with inner products. For example,

With four-momentum

Often, when using the Dirac equation and solving for cross sections, one finds the slash notation used on four-momentum:

using the Dirac basis for the 's,

as well as the definition of four momentum

We see explicitly that

Similar results hold in other bases, such as the Weyl basis.

See also

References

Chord chart

A chord chart (or chart) is a form of musical notation that describes the basic harmonic and rhythmic information for a song or tune. It is the most common form of notation used by professional session musicians playing jazz or popular music. It is intended primarily for a rhythm section (usually consisting of piano, guitar, drums and bass). In these genres the musicians are expected to be able to improvise the actual notes used for the chords and the appropriate ornamentation, counter melody or bassline.

In some chord charts, the harmony is given as a series of chord symbols above a traditional musical staff. The rhythmic information can be very specific and written using a form of traditional notation, sometimes called rhythmic notation, or it can be completely unspecified using slash notation, allowing the musician to fill the bar with chords or fills any way he or she sees fit (called "comping"). In Nashville notation the key is left unspecified on the chart by substituting numbers for chord names. This facilitates on-the-spot key changes to songs.

Indian Institute of Science

Indian Institute of Science (IISc) is a public university for scientific research and higher education located in Bangalore, India. Established in 1909 with active support from Jamsetji Tata and H.H. Sir Krishnaraja Wodeyar IV, the Maharaja of Mysore. It is also locally known as the "Tata Institute". It acquired the status of a Deemed University in 1958. IISc is widely regarded as India's finest institution in its field, and has been ranked at number 11 and 18 worldwide (and ranked 3rd and 6th in Asia) when considering the criteria of Citations per Faculty in 2014 and 2015 respectively. IISc was the first Indian institute to feature on Times Higher Education World University Rankings for engineering and technology in the year 2015-16 at 99th position. IISc has been ranked number 1 and 4 in the BRICS and Asian region respectively while considering the criteria of Papers per Faculty in 2015. IISc has also been ranked 6th in the criteria of research by the Times Higher Education Rankings for the BRICS & Emerging Economies Rankings 2016 IISc has made significant contribution to advanced computing, space, and nuclear technologies.

Relativistic quantum mechanics

In physics, relativistic quantum mechanics (RQM) is any Poincaré covariant formulation of quantum mechanics (QM). This theory is applicable to massive particles propagating at all velocities up to those comparable to the speed of light c, and can accommodate massless particles. The theory has application in high energy physics,particle physics and accelerator physics, as well as atomic physics, chemistry and condensed matter physics.Non-relativistic quantum mechanics refers to the mathematical formulation of quantum mechanics applied in the context of Galilean relativity, more specifically quantizing the equations of classical mechanics by replacing dynamical variables by operators. Relativistic quantum mechanics (RQM) is quantum mechanics applied with special relativity, but not general relativity. An attempt to incorporate general relativity into quantum theory is the subject of quantum gravity, an unsolved problem in physics, although some theories, such as the Kaluza-Klein, have been proposed but are unfounded and without proof. Although the earlier formulations, like the Schrödinger picture and Heisenberg picture were originally formulated in a non-relativistic background, these pictures of quantum mechanics also apply with special relativity.

Apoorva D. Patel

Apoorva D. Patel is a Professor at the Centre for High Energy Physics, Indian Institute of Science, Bangalore. He is notable for his work on quantum algorithms, and the application of information theory concepts to understand the structure of genetic languages. His major field of work has been the theory of quantum chromodynamics, where he has used lattice gauge theory techniques to investigate spectral properties, phase transitions, and matrix elements.

Education

He obtained his MSc in Physics (1980) from the Indian Institute of Technology Bombay, and PhD in Physics from the California Institute of Technology under Geoffrey C. Fox (1984), with a thesis entitled: Monte Carlo Renormalisation Group for Lattice QCD.

Career

He was a Scientific Associate, Theory Division, CERN, Geneva, Switzerland, 1987–1989, and the in 1989 he joined the Indian Institute of Science, Bangalore, as a faculty member.

Personal life

In 1989 he married Rashmi, a surgeon specializing in laparoscopy and endosurgery. His son, Aavishkar, was born in 1990.