Many thanks to my qualification committee: Andy Strominger, Daniel Jafferis, and Matt Reece! They were awesome professors during this past year and have made my G1 year most memorable. I am honored to have them as my mentors in the years to come.

I look forward to filing my first PhD Candidate Progress Report on August 1st !

July 30, 2013

Dot Products in Special Relativity

Sabrina Gonzalez Pasterski

I present a derivation of the Minkowski metric and visualizations of the space-time dot product.

Dot Products in Special Relativity

Sabrina Gonzalez Pasterski

I present a derivation of the Minkowski metric and visualizations of the space-time dot product.

August 1, 2013

Degeneracy vs. Energy Level Scaling for Hydrogen

Sabrina Gonzalez Pasterski

I explore the relationship between degeneracy and energy for the Hydrogen atom.

Degeneracy vs. Energy Level Scaling for Hydrogen

Sabrina Gonzalez Pasterski

I explore the relationship between degeneracy and energy for the Hydrogen atom.

September 8, 2013

Wavefunctions and the Hamilton-Jacobi Equation

Sabrina Gonzalez Pasterski

I show how the differential equation governing a distribution over classical trajectories is consistent with the quantum Schrodinger Equation in the h --> 0 limit.

Wavefunctions and the Hamilton-Jacobi Equation

Sabrina Gonzalez Pasterski

I show how the differential equation governing a distribution over classical trajectories is consistent with the quantum Schrodinger Equation in the h --> 0 limit.

March 2, 2014

Covariant Derivatives and the Hamilton-Jacobi Equation

Sabrina Gonzalez Pasterski

I define a covariant derivative to simplify how higher order derivatives act on a classical generating function.

Covariant Derivatives and the Hamilton-Jacobi Equation

Sabrina Gonzalez Pasterski

I define a covariant derivative to simplify how higher order derivatives act on a classical generating function.

March 2, 2014

Expectation Values from the Hamilton-Jacobi Equation

Sabrina Gonzalez Pasterski

I use the classical Hamilton-Jacobi Equation to formulate a definition for operator expectation values consistent with those for quantum operators.

Expectation Values from the Hamilton-Jacobi Equation

Sabrina Gonzalez Pasterski

I use the classical Hamilton-Jacobi Equation to formulate a definition for operator expectation values consistent with those for quantum operators.

March 17, 2014

Fields with a Gaussian Measure

Sabrina Gonzalez Pasterski

A calculation.

Fields with a Gaussian Measure

Sabrina Gonzalez Pasterski

A calculation.

August 4, 2013

Conformal Mapping of Displacement Vectors

Sabrina Gonzalez Pasterski

I explore the asymmetry between displacements in space and time for motion in one dimension.

Conformal Mapping of Displacement Vectors

Sabrina Gonzalez Pasterski

I explore the asymmetry between displacements in space and time for motion in one dimension.

August 2, 2013

An Alternate Approach for Finding an Orthogonal Basis

Sabrina Gonzalez Pasterski

I present an alternative to the Gram-Schmidt method for finding a basis of orthogonal vectors spanning the same space as a set of starting vectors.

An Alternate Approach for Finding an Orthogonal Basis

Sabrina Gonzalez Pasterski

I present an alternative to the Gram-Schmidt method for finding a basis of orthogonal vectors spanning the same space as a set of starting vectors.

August 5, 2013

Space and Time

Sabrina Gonzalez Pasterski

I arrive at Maxwell’s Equations, gauge invariance, and the force law for charges, starting from a conserved current.

Space and Time

Sabrina Gonzalez Pasterski

I arrive at Maxwell’s Equations, gauge invariance, and the force law for charges, starting from a conserved current.

September 8, 2013

Solving the Shrodinger Equation Using a Complex Gauge

Sabrina Gonzalez Pasterski

I show a quick route to the n = l + 1 wave functions and energies for the Hydrogen atom using a method which is also applied to find the ground state of the simple harmonic oscillator.

Solving the Shrodinger Equation Using a Complex Gauge

Sabrina Gonzalez Pasterski

I show a quick route to the n = l + 1 wave functions and energies for the Hydrogen atom using a method which is also applied to find the ground state of the simple harmonic oscillator.

June 12, 2014

Semiclassical Virasoro Symmetry of the Quantum Gravity S-Matrix

D. Kapec, V. Lysov, S. Pasterski and A. Strominger

It is shown that the tree-level S-matrix for quantum gravity in four-dimensional Minkowski space has a Virasoro symmetry which acts on the conformal sphere at null infinity.

(Accepted for publication in JHEP on July 17, 2014)

Semiclassical Virasoro Symmetry of the Quantum Gravity S-Matrix

D. Kapec, V. Lysov, S. Pasterski and A. Strominger

It is shown that the tree-level S-matrix for quantum gravity in four-dimensional Minkowski space has a Virasoro symmetry which acts on the conformal sphere at null infinity.

(Accepted for publication in JHEP on July 17, 2014)

April 20, 2014

Gaussian Measures and the QM Oscillator

Sabrina Gonzalez Pasterski

In this paper, I show how probability densities associated with a Gaussian field can be expressed in terms of the Boltzmann heat kernel.

Gaussian Measures and the QM Oscillator

Sabrina Gonzalez Pasterski

In this paper, I show how probability densities associated with a Gaussian field can be expressed in terms of the Boltzmann heat kernel.

March 31, 2014

Soft Theorems and Symmetry

Sabrina Gonzalez Pasterski

I examine the connection between symmetries and soft factors for the case of graviton scattering.

Soft Theorems and Symmetry

Sabrina Gonzalez Pasterski

I examine the connection between symmetries and soft factors for the case of graviton scattering.

March 10, 2014

Gaussian Measures and Commutators

Sabrina Gonzalez Pasterski

I show how defining a field with a gaussian measure gives rise to a classical interpretation of the equal time commutation relations for a field and its derivative.

Gaussian Measures and Commutators

Sabrina Gonzalez Pasterski

I show how defining a field with a gaussian measure gives rise to a classical interpretation of the equal time commutation relations for a field and its derivative.

March 31, 2014

From Gaussian Measures to SDE

Sabrina Gonzalez Pasterski

In this paper, I show how a field with gaussian measure can give the Schwinger-Dyson Equations of QFT in Wick rotated time.

From Gaussian Measures to SDE

Sabrina Gonzalez Pasterski

In this paper, I show how a field with gaussian measure can give the Schwinger-Dyson Equations of QFT in Wick rotated time.

July 14, 2013

Hamilton’s Equations of Motion

Sabrina Gonzalez Pasterski

I motivate Hamilton’s equations of motion using a geometrical picture of contours in phase space. The following considers a single cartesian coordinate x with conjugate momentum p.

Hamilton’s Equations of Motion

Sabrina Gonzalez Pasterski

I motivate Hamilton’s equations of motion using a geometrical picture of contours in phase space. The following considers a single cartesian coordinate x with conjugate momentum p.

July 23, 2013

Visualization for Spin-1/2 Inner Products

Sabrina Gonzalez Pasterski

I present a geometrical visualization for the magnitude of the inner product of two spin-1/2 states.

Visualization for Spin-1/2 Inner Products

Sabrina Gonzalez Pasterski

I present a geometrical visualization for the magnitude of the inner product of two spin-1/2 states.

July 24, 2013

Motivating Special Relativity using Linear Algebra

Sabrina Gonzalez Pasterski

I present a geometrical derivation of results from Special Relativity for a single spatial coordinate.

Motivating Special Relativity using Linear Algebra

Sabrina Gonzalez Pasterski

I present a geometrical derivation of results from Special Relativity for a single spatial coordinate.

July 27, 2013

Position as a Single-Valued Function of Time

Sabrina Gonzalez Pasterski

I present a geometrical illustration of how the speed limit in Special Relativity requires position to be a single-valued function of time in any reference frame.

Position as a Single-Valued Function of Time

Sabrina Gonzalez Pasterski

I present a geometrical illustration of how the speed limit in Special Relativity requires position to be a single-valued function of time in any reference frame.

July 30, 2013

The Schrodinger Equation and Phase Space

Sabrina Gonzalez Pasterski

I arrive at the Schrodinger Equation given a particular form for probabilities in phase space.

The Schrodinger Equation and Phase Space

Sabrina Gonzalez Pasterski

I arrive at the Schrodinger Equation given a particular form for probabilities in phase space.

February 28, 2014

Insights into Becoming a Theoretical Physicist

Sabrina Gonzalez Pasterski

An inspirational speech given in Princeton, NJ.

I donated my $500 honorarium to Harvard Physics.

Insights into Becoming a Theoretical Physicist

Sabrina Gonzalez Pasterski

An inspirational speech given in Princeton, NJ.

I donated my $500 honorarium to Harvard Physics.

April 21, 2014

Gaussian Measures in Quantum Theory

Sabrina Gonzalez Pasterski

Invited talk. Harvard String Group.

Gaussian Measures in Quantum Theory

Sabrina Gonzalez Pasterski

Invited talk. Harvard String Group.

My most recent G1 adventure: the PhD Qualifying Examination !

July 14, 2014

Low’s Subleading Soft Theorem as a Symmetry of QED

V. Lysov, S. Pasterski and A. Strominger

It was shown by F. Low in the 1950s that the subleading terms of soft photon S-matrix elements obey a universal linear relation. In this paper we give a new interpretation to this old relation, for the case of massless QED, as an infinitesimal symmetry of the S-matrix.

(Submitted for publication at the request of PRL on July 16, 2014)

Low’s Subleading Soft Theorem as a Symmetry of QED

V. Lysov, S. Pasterski and A. Strominger

It was shown by F. Low in the 1950s that the subleading terms of soft photon S-matrix elements obey a universal linear relation. In this paper we give a new interpretation to this old relation, for the case of massless QED, as an infinitesimal symmetry of the S-matrix.

(Submitted for publication at the request of PRL on July 16, 2014)

in progress

S. Pasterski, A. Porfyriadis and A. Strominger

S. Pasterski, A. Porfyriadis and A. Strominger

coming soon...