What does DS mean in integrals?
differential element
The line integral of f(x,y) along C is denoted by: The differential element is ds. This is the fact that we are moving along the curve, C, instead dx for the x-axis, or dy for the y-axis. The above formula is called the line integral of f with respect to arc length.
Why does Wick rotate?
Wick rotation is called a rotation because when we represent complex numbers as a plane, the multiplication of a complex number by i is equivalent to rotating the vector representing that number by an angle of π/2 about the origin.
What is a propagator in quantum mechanics?
In quantum mechanics and quantum field theory, the propagator is a function that specifies the probability amplitude for a particle to travel from one place to another in a given period of time, or to travel with a certain energy and momentum.
What is Stephen Hawking’s imaginary time?
Stephen Hawking popularized the concept of imaginary time in his book The Universe in a Nutshell. “One might think this means that imaginary numbers are just a mathematical game having nothing to do with the real world. From the viewpoint of positivist philosophy, however, one cannot determine what is real.
What is volume integral in physics?
In mathematics (particularly multivariable calculus), a volume integral (∭) refers to an integral over a 3-dimensional domain; that is, it is a special case of multiple integrals. Volume integrals are especially important in physics for many applications, for example, to calculate flux densities.
What is line surface and volume integral?
A line integral is an integral where the function to be integrated is evaluated along a curve and a surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analog of the line integral.
What is Euclidean time?
Euclidean time is obtained from Lorentzian time by a Wick rotation in the complex t plane, and enters into the resulting equations exactly in the same way as a spatial coordinate x.