Abstract:We show that the one-loop on-shell four-point scattering amplitude of massless φ 4 scalar field theory in 4D Minkowski space time, when Mellin transformed to the Celestial sphere at infinity, transforms covariantly under the global conformal group (SL(2, C)) on the sphere. The unitarity of the four-point scalar amplitudes is recast into this Mellin basis. We show that the same conformal structure also appears for the two-loop Mellin amplitude. Finally we comment on some universal structure for all loop four-point Mellin amplitudes specific to this theory.
We obtain the subleading soft theorem for a generic theory of quantum gravity, for arbitrary number of soft photons and gravitons and for arbitrary number of finite energy particles with arbitrary mass and spin when all the soft particles are soft in the same rate. This result is valid at tree level for spacetime dimensions equal to four and five and to all loop orders in spacetime dimensions greater than five. We verify that in classical limit, low energy photon and graviton radiation decouple from each other.
We study the loop level asymptotic conservation law proposed by Campiglia and Laddha [1] for massless scalar QED in presence of dynamical gravity. We show that the equivalence between the loop level Ward identity and the Sahoo-Sen soft photon theorem [2] continues to hold. In presence of gravity, the new feature is that photons also acquire a dressing due to long range gravitational force and contribute to the charge. Similar to the massive case, the terms in the asymptotic charge are directly related to the dressing of scalars and photons due to long range forces.
Motivated by Campiglia and Laddha [1], we show that the Sahoo-Sen soft photon theorem [2] for loop amplitudes is equivalent to an asymptotic conservation law. This asymptotic charge is directly related to the dressing of fields due to long range forces exclusively present in four spacetime dimensions. In presence of gravity, the new feature is that photons also acquire a dressing due to long range gravitational force and this dressing contributes to the asymptotic charge.
We study the second derivative effects on the constitutive relations of an uncharged parity-even Galilean fluid using the null fluid framework. Null fluids are an equivalent representation of Galilean fluids in terms of a higher dimensional relativistic fluid, which makes the Galilean symmetries manifest and tractable. The analysis is based on the off-shell formalism of hydrodynamics. We use this formalism to work out a generic algorithm to obtain the constitutive relations of a Galilean fluid up to arbitrarily high derivative orders, and later specialize to second order. Finally, we study the Stokes' law which determines the drag force on an object moving through a fluid, in presence of certain second order terms. We identify the second order transport coefficients which leave the drag force invariant.
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