James Vernon Taylor (born March 12, 1948) is an American singer-songwriter and guitarist. A five-time Grammy Award winner, Taylor was inducted into the Rock and Roll Hall of Fame in 2000. Taylor achieved his breakthrough in 1970 with the No. 3 single "Fire and Rain" and had his first No. 1 hit the following year with "You've Got a Friend", a recording of Carole King's classic song. His 1976 Greatest Hits album was certified Diamond and has sold 12 million US copies. Following his 1977 album, JT, he has retained a large audience over the decades. His commercial achievements declined slightly until...

In quantum field theory, the Gupta–Bleuler formalism is a way of quantizing the electromagnetic field. The formulation is due to theoretical physicists Suraj N. Gupta and Konrad Bleuler. Let's start with a single photon first. A basis of the one-photon vector space (we'll explain why it's not a Hilbert space below) is given by the eigenstates |k,εμ〉 where k, the 4-momentum is null (k2=0) and the k0 component, the energy, is positive and εμ is the unit polarization vector and the index μ ranges from 0 to 3. So, k is uniquely determined by the spatial momentum . Using the bra–ket notation, we equip...

In mathematics, the Moyal product (also called the star product or Weyl-Groenewold product) is perhaps the best-known example of a phase-space star product. It is an associative, non-commutative product, ★, on the functions on ℝ2n, equipped with its Poisson bracket (with a generalization to symplectic manifolds, described below). == Historical comments == The Moyal product is named after José Enrique Moyal, but is also sometimes called the Weyl-Groenewold product as it was introduced by H. J. Groenewold in his 1946 doctoral dissertation, in a trenchant appreciation of the Weyl correspondence. Moyal...