Stanley Mandelstam

Research Interests

My research concerns string theory. At present I am interested in finding an explicit expression for the n-loop superstring amplitude and proving that it is finite. My field of research is particle theory, more specifically string theory. I am also interested in the recent results of Seiberg and Witten in supersymmetric field theories.

Current Projects

My present research concerns the problem of topology changing in string theory. It is currently believed that one has to sum over all string backgrounds and all topologies in doing the functional integral. I suspect that certain singular string backgrounds may be equivalent to topology changes, and that it is consequently only necessary to sum over string backgrounds. As a start I am investigating topology changes in two-dimensional target spaces. I am also interested in Seiberg-Witten invariants. Although much has been learned, some basic questions remain, and I hope to be able at least to understand the simpler of these questions.

http://www.physics.berkeley.edu/research/faculty/mandelstam.html



Stanley Mandelstam (b. 1928, Johannesburg) is a South African-born theoretical physicist. He introduced the relativistically invariant Mandelstam variables into particle physics in 1958 as a convenient coordinate system for formulating his double dispersion relations. The double dispersion relations were a central tool in the bootstrap program which sought to formulate a consistent theory of infinitely many particle types of increasing spin.

Mandelstam, along with Tullio Regge, was responsible for the Regge theory of strong interaction phenomenology. He reinterpreted the analytic growth rate of the scattering amplitude as a function of the cosine of the scattering angle as the power law for the falloff of scattering amplitudes at high energy. Along with the double dispersion relation, Regge theory allowed theorists to find sufficient analytic constraints on scattering amplitudes of bound states to formulate a theory in which there are infintely many particle types, none of which are fundamental.

After Veneziano constructed the first tree-level scattering amplitude describing infinitely many particle types, what was recognized almost immediately as a string scattering amplitude, Mandelstam continued to make crucial contributions. He interpreted the Virasoro algebra discovered in consistency conditions as a geometrical symmetry of a world-sheet conformal field theory, formulating string theory in terms of two dimensional quantum field theory. He used the conformal invariance to calculate tree level string amplitudes on many worldsheet domains. Mandelstam was the first to explicitly construct the fermion scattering amplitudes in the Ramond and Neveu-Schwarz sectors of superstring theory, and later gave arguments for the finiteness of string perturbation theory.

In quantum field theory, Mandelstam and independently Sidney Coleman extended work of Tony Skyrme to show that the two dimensional quantum Sine-Gordon model is equivalently described by a thirring model whose fermions are the kinks. He also demonstrated that the 4d N=4 supersymmetric gauge theory is power counting finite, proving that this theory is scale invariant to all orders of perturbation theory, the first example of a field theory where all the infinities in feynman diagrams cancel.

Among his students at Berkeley are Joseph Polchinski and Charles Thorn.

Education: Witwatersrand (BSc, 1952); Trinity College, Cambridge (BA, 1954); Birmingham University (PhD, 1956).

Intellectual Defeatism

Just wanted to say it has been quite busy here because of the work having come back from vacation and preparing for my daughter in law and son's twins, which are to arrive any day now.

Intellectual defeatism

This statement reminded me of the idea about what is left for some to ponder, while we rely on our instincts to peer into the unknown, and hopefully land in a place that is correlated somehow in our future.

This again is being bold to me, because there are no rules here about what a schooling may provide for, what allows an individual the freedoms to explore great unknowns for them. For sure education then comes to check what these instincts have provided, and while being free to roam the world, sometimes it does find a "certain resonance" in what is out there.

Is this then a sign of what intellectual defeatism is about?

I want to give an example here about my perceptions about what sits in the valleys in terms of topological formations, that until now I had no way of knowing would become a suitable explanation for me, "about what is possible" even thought this represented a many possibility explanation in terms of outcomes.

Observables of Quantum Gravity

Scientists should be bold. They are expected to think out of the box, and to pursue their ideas until these either trickle down into a new stream, or dry out in the sand. Of course, not everybody can be a genuine “seer”: the progress of science requires few seers and many good soldiers who do the lower-level, dirty work. Even soldiers, however, are expected to put their own creativity in the process now and then -and that is why doing science is appealing even to us mortals.

To Be Bold

One possible way the Higgs boson might be produced at the Large Hadron Collider.


"Observables of Quantum Gravity," is a strange title to me, since we are looking at perspectives that are, how would one say, limited?

Where is such a focus located that we make talk of observables? Can such an abstraction be made then and used here, that we may call it, "mathematics of abstraction" and can arise from a "foundational basis" other then all the standard model distributed in particle attributes?

Observables of Quantum Gravity at the LHC
Sabine Hossenfelder

Perimeter Institute, Ontario, Canada

The search for a satisfying theory that unifies general relativity with quantum field theory is one of the major tasks for physicists in the 21st century. Within the last decade, the phenomenology of quantum gravity and string theory has been examined from various points of view, providing new perspectives and testable predictions. I will give a short introduction into these effective models which allow to extend the standard model and include the expected effects of the underlying fundamental theory. I will talk about models with extra dimensions, models with a minimal length scale and those with a deformation of Lorentz-invariance. The focus is on observable consequences, such as graviton and black hole production, black hole decays, and modifications of standard-model cross-sections.

So while we have created the conditions for an experimental framework, is this what is happening in nature? We are simulating the cosmos in it's interactions, so how is it that we can bring the cosmos down to earth? How is it that we can bring the cosmos down to the level of mind in it's abstractions that we do not just call it a flight of fancy, but of one that arises in mind based on the very foundations on the formation of this universe?

Fathers of Confederation

Robert Harris's painting of the Fathers of Confederation. The scene is an amalgamation of the Charlottetown and Quebec City conference sites and attendees.

Colonial organization

All the colonies which would become involved in Canadian Confederation in 1867 were initially part of New France and were ruled by France. The British Empire’s first acquisition in what would become Canada was Acadia, acquired by the 1713 Treaty of Utrecht (though the Acadian population retained loyalty to New France, and was eventually expelled by the British in the 1755 Great Upheaval). The British renamed Acadia Nova Scotia. The rest of New France was acquired by the British Empire by the Treaty of Paris (1763), which ended the Seven Years' War. Most of New France became the Province of Quebec, while present-day New Brunswick was annexed to Nova Scotia. In 1769, present-day Prince Edward Island, which had been a part of Acadia, was renamed “St John’s Island” and organized as a separate colony (it was renamed PEI in 1798 in honour of Prince Edward, Duke of Kent and Strathearn).

In the wake of the American Revolution, approximately 50,000 United Empire Loyalists fled to British North America. The Loyalists were unwelcome in Nova Scotia, so the British created the separate colony of New Brunswick for them in 1784. Most of the Loyalists settled in the Province of Quebec, which in 1791 was separated into a predominantly-English Upper Canada and a predominantly-French Lower Canada by the Constitutional Act of 1791.
Canadian Territory at Confederation.

Following the Rebellions of 1837, Lord Durham in his famous Report on the Affairs of British North America, recommended that Upper Canada and Lower Canada should be joined to form the Province of Canada and that the new province should have responsible government. As a result of Durham’s report, the British Parliament passed the Act of Union 1840, and the Province of Canada was formed in 1841. The new province was divided into two parts: Canada West (the former Upper Canada) and Canada East (the former Lower Canada). Ministerial responsibility was finally granted by Governor General Lord Elgin in 1848, first to Nova Scotia and then to Canada. In the following years, the British would extend responsible government to Prince Edward Island (1851), New Brunswick (1854), and Newfoundland (1855).

The remainder of modern-day Canada was made up of Rupert's Land and the North-Western Territory (both of which were controlled by the Hudson's Bay Company and ceded to Canada in 1870) and the Arctic Islands, which were under direct British control and became part of Canada in 1880. The area which constitutes modern-day British Columbia was the separate Colony of British Columbia (formed in 1858, in an area where the Crown had previously granted a monopoly to the Hudson's Bay Company), with the Colony of Vancouver Island (formed 1849) constituting a separate crown colony until its absorption by the Colony of British Columbia in 1866.

John A. Macdonald became the first prime minister of Canada.


The shear number of people in the United States at approx. 200 million,can be an reminder of what "we", in the approx. same land mass of Canada can be compared to the United States. Our paltry 36 million "being overshadowed" might be better understood from that perspective.

Happy Canada Day

Coastal Highway Views

Just before entering Malibu along the coastal highway of California.