The subject has two principal parts: Lagrangian mechanics and Hamiltonian mechanics, both are tightly intertwined.

In quantum field theory, chiral symmetry is a possible symmetry of the Lagrangian under which the left-handed and right-handed parts of Dirac fields transform independently.

Let us refer to such a regularization as the minimal realistic regularization, and start searching for the corresponding, modified free-field parts of the QED Lagrangian density.

What we have left as reasonably comparable are four classes: ( 1 ) body parts and products, which with a proportionally nearly even representation ( 51 terms out of 253, 25 out of 100 ) come out with nearly even ratios ; ;

and it is as if the only stable relation left among the different parts of the picture is the ambivalent and ambiguous one that each has with the surface.

There are also a few parts of both medieval city walls left, most of them integrated into more recent buildings, but some others still visible.

The city is built on a bend of the river Garonne, and is divided into two parts: the right bank to the east and left bank in the west.

Octavian was not present, but at the next meeting made a reply of such a nature that the consuls both left Rome to join Antony ; and Antony, when he heard of it, after publicly divorcing Octavia, came at once to Ephesus with Cleopatra, where a vast fleet was gathered from all parts of the East, of which Cleopatra furnished a large proportion.

The Jewish people still await the Messiah's first coming, while Christians await his second coming, when they believe he will fulfill those parts of Messianic prophecy left unfulfilled in the first century AD.

As Speerstra and also note, the compass of the keyboard parts of Bach's six organ trio sonatas BWV 525 – 530 rarely go below the tenor C, so could have been played on a single manual pedal clavichord, by moving the left hand down an octave, a customary practice in the 18th century.

No parts are left at the airport after conversion from aircraft to ground vehicle, as the main wing and tail retract into the vehicle body.

The Marlins also lost key parts of their second championship team, Ugueth Urbina and Iván Rodríguez left via free agency ( signed by the Detroit Tigers ).

The Franconian lands are situated north and south of the winding Main River, which together with the left ( southern ) Regnitz tributary, including its Rednitz and Pegnitz headstreams, drains the most parts of Franconia.

These works also left Europe and were imported to those parts of Latin America controlled by the Spanish and Portuguese empires and the parts of North America controlled by the British and French empires.

) green, with some parts left blued.

This left the early universe with a very similar ratio of hydrogen / helium as is observed today ( 3 parts hydrogen to 1 part helium-4 by mass ), with nearly all the neutrons in the universe trapped in helium-4.

If left untreated, this growth can spread beyond the lung in a process called metastasis into nearby tissue and, eventually, into other parts of the body.

In this case, four different numbers were inserted, with dots between them: the rightmost one is a timestamp of the number of seconds since January 1, 1970, known as the Unix epoch ; to the left of it is the process ID of the program that generated the message ( on servers running Unix or Linux, each process has a number which is unique among the processes in progress at any moment, though they do repeat over time ); to the left of that is a count of the number of messages generated so far by the current process ; and the leftmost number is the number of parts in the current message that have been generated so far.

Moreover, lack of foreign exchange to purchase spare parts and oil for electricity generation left many factories idle.

In the left foreground is Leipziger Platz, while in the right foreground are parts of the Sony and Beisheim Centers.

A secondary benefit may be some reduction in friction with the cylinder wall, however as most of this is due to the parts of the piston that are left behind, the benefit is minor.

However due to many cultural differences a system of passively co-existing communities, segregated along racial lines has emerged in parts of the United Kingdom, with minority communities being left " marooned outside the mainstream ”.

Asau, with the Potlatch sawmillers and Samoa Forest Products, was one of the busiest parts of Savai ' i in the 1960s and 1970s ; however, the departure of Potlatch and the scaling down of the sawmill has left Asau a ghost town in recent years.

Though most of the pattern is removed from PAL and NTSC-encoded signals with a comb filter ( designed to segregate the two signals where the luma spectrum may overlap into the spectral space used by the chroma ) by modern displays, some can still be left in certain parts of the picture.

Effectively, the list is divided into two parts: the sublist of items already sorted, which is built up from left to right and is found at the beginning, and the sublist of items remaining to be sorted, occupying the remainder of the array.

Heracles succeeded in freeing only Theseus, and left behind his buttocks attached to the rocks-from which Theseus came to be called hypolispos, meaning " with hinder parts rubbed smooth.

Other parts of the Kennedy health plan would entail federal grants of 750 million to 1 billion dollars over the next 10 years.

The quest for holism leads most anthropologists to study a particular place, problem or phenomenon in detail, using a variety of methods, over a more extensive period than normal in many parts of academia.

In 1061, Abu Bakr ibn Umar made a division of the power he had established, handing over the more-settled parts to his cousin Yusuf ibn Tashfin, as viceroy, resigning to him also his favourite wife Zainab.

* 1859 – A geomagnetic storm causes the Aurora Borealis to shine so brightly that it is seen clearly over parts of USA, Europe, and even as far away as Japan.

Although game reports and social reactions are common parts of many A & E contributions, it has also, over the years, become a testing ground for new ideas on the development of the RPG as a genre and an art form.

Similarly, the language spread to numerous other parts of the world as a result of British trade and colonization elsewhere and the spread of the former British Empire, which, by 1921, held sway over a population of 470 – 570 million people, approximately a quarter of the world's population at that time.

Within five days after the beginning of their terms, the four Aediles ( two Plebeian, two Curule ) were required to determine, by lot or by agreement among themselves, what parts of the city each should hold jurisdiction over.

" The frolic went all over England ," says Roger North ; and the addresses of the Abhorrers which reached the king from all parts of the country formed a counterblast to those of the Petitioners.

It is defined as the range of speeds between the critical Mach number, when some parts of the airflow over an aircraft become supersonic, and a higher speed, typically near Mach 1. 2, when all of the airflow is supersonic.

Consequently such meters would normally have a non linear scale, but the iron parts are usually modified in shape to make the scale fairly linear over most of its range.

The effects of the afore-mentioned high-pressure area did not reach the southern parts of the Baltic Sea, and thus the entire sea did not freeze over.

However, it is also possible to divide the book into three parts rather than four by combining the sections treating David and Solomon, since they both ruled over a combined Judah and Israel, unlike the last section that contains the chronicle of the Davidic kings who ruled the Kingdom of Judah alone.

* The Duchy of Brabant, a duchy of the Holy Roman Empire between 1183 – 1648 covering parts of the Netherlands and Belgium, ruled over by the Dukes of Brabant

The government took no action, and handed the final parts of Bakassi over to Cameroon on 14 August 2008 as planned, but a Federal High Court had stated this should be delayed until all accommodations for resettled Bakassians had been settled ; the government did not seem to plan to heed this court order, and did set the necessary mechanisms into motion to override it.

Some parts of the earth have more or less the same kind of abiotic and biotic factors spread over a large area, creating a typical ecosystem over that area.

At first the new style took over Baroque forms — the ternary da capo aria and the sinfonia and concerto — but composed with simpler parts, more notated ornamentation and more emphatic division into sections.

The princes of Bribir from the Šubić family became particularly influential, asserting control over large parts of Dalmatia, Slavonia and Bosnia.

The town included a much larger area than the present city, with various outlying parts becoming independent towns over the years: Newton ( originally Cambridge Village, then Newtown ) in 1688, Lexington ( Cambridge Farms ) in 1712, and both West Cambridge ( originally Menotomy ) and Brighton ( Little Cambridge ) in 1807.

Corporatism refers to a form of collectivism that views the whole as being greater than the sum of its individual parts, and gives priority to group rights over individual rights.

In 960, the Song Dynasty gained power over most of China and established its capital in Kaifeng ( later known as Bianjing ), starting a period of economic prosperity, while the Khitan Liao Dynasty ruled over Manchuria, present-day Mongolia, and parts of Northern China.

Soon however, they began quarrelling over which parts of the African provinces belonged to Carthage, and thus Constantine, and that which belonged to Italy, and therefore Constans.

Cartoons were typically used in the production of frescoes, to accurately link the component parts of the composition when painted on damp plaster over a series of days ( giornate ).

Soon however, they began quarrelling over which parts of the African provinces belonged to Carthage, and thus Constantine, and that which belonged to Italy, and therefore Constans.