On Generalized Uncertainty Principle

Understand

We study generalized uncertainty principle through the basic concepts of limit and Fourier transformation and analyze both the quantum theory of gravity and string theory from the perspective of complex function theory.

• Motivated from the noncommutative nature of string theory, we have proposed a UV/IR mixing dependent function $ \tilde{\delta}(\Delta x,\Delta k, \epsilon) $.
• For a given $ \tilde{\delta}(\Delta x,\Delta k, \epsilon) $, we arrived at the string uncertainty principle from the analyticity condition of a complex function, which depends upon UV cut-off of the theory.
• This non trivially modifies the quantum measurements, black hole physics and short distance geometries.